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Benedictine University MGT 150 Business Statistics I, Sec. B
Spring, 2017Class Location: GN-312
Class Meeting Times: TuTh-8:00Office Hours: MW–10:00-1:00, TuTh–9:30-11:00; GN-166
Instructor: Jeffrey M. MaduraB.A. University of Notre DameM.B.A. Northwestern University
C.P.A. State of IllinoisContact Information: 630-829-6467 / [email protected]: http://www.ben.edu/faculty/jmadura/home.htm
Course Description: (from the Catalog) Basic course in statistical technique, includes measures of central tendency, variability, probability theory, sampling, estimation and hypothesis testing. Computational, Mathematical and Analytical Mode of Inquiry (QCM).Three semester hours.
(Instructor's description) This is a course in introductory statistics. The orientation is toward applications and problem-solving, not mathematical theory. The instructor intends that students gain an appreciation for the usefulness of statistical methods in analyzing data commonly encountered in business and the social and natural sciences. The course is a framework within which students may learn the subject matter. This framework consists of a program of study, opportunity for questions/discussion, explanation, and evaluative activities (quizzes). The major topics are:
o Data and Statisticso Descriptive Statistics: Tabular and Graphical Presentationso Descriptive Statistics: Numerical Measureso Introduction to Probabilityo Discrete Probability Distributionso Continuous Probability Distributionso Sampling and Sampling Distributionso Interval Estimation, Means and Proportionso Hypothesis Tests, Means and Proportions
Learning Objectives: below
Course Expectations: The instructor expects students to learn the terminology, understand the concepts, and apply the computational procedures described at the end of each of the five parts of the Course Outline that follows this syllabus.
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College of Business Learning Objectives: The course addresses the following College of Business Program Objectives:Students in this program will receive a thorough grounding in Mathematics and Statistics.
IDEA objectives: This course emphasizes the following IDEA objectives:
Learning fundamental principles, generalizations, or theories.Learning to apply course material to improve thinking, problem-solving, and
decision-making.Developing specific skills, competencies and points of view needed by professionals
in the fields most closely related to this course. Prerequisites: MATH 105 or MATH 110.
Software: Familiarity with Microsoft Excel is expected.
Required Text and Materials: Textbook: Modern Business Statistics with Microsoft Office Excel, 5th edition;
Anderson, Sweeney & Williams, South-Western/Cengage, 2015;ISBN: 978-1-285-43330-1 (hard cover)
Other: Aplia interactive learning/assignment system. Aplia includes the textbook as an e-book.
TI-83 or TI-84 calculator.
Course Schedule: The course is divided into five three-week parts, with a quiz at the end of each part. Dates are subject to change.
Week 1-4 starts 1/17 Introduction; Descriptive StatisticsWeek 5-7 2/13 Probability; Tests for DependenceWeek 8-10 3/6 Permutations and Combination; Binomial and Normal
DistributionsWeek 11-13 4/3 Estimation and Hypothesis Testing—MeansWeek 14-15 4/24 Estimation and Hypothesis Testing—Proportions
Quizzes 1-4 will be on the Thursday of weeks 4, 7, 10, and 13.Quiz 5 will be on the date and time scheduled for the final exam.Your average on the quizzes will constitute 2/3 of the course grade.
Grade requirements: A–90%, B–80%, C–60%, D–50%. There may also be other assignments requiring analysis of data using Excel. There will be a term project on Critical Thinking, with weight equal to one quiz. It is the responsibility of any student who is unsure of the grading scale, course requirements, or anything else in this course outline to ask the instructor for clarification.
Homework Assignments: There will be 10-15 Aplia homework assignments. Due dates are listed in the Aplia system. The assignments will constitute 1/3 of the course grade. To accommodate the occasional instance when you cannot meet an Aplia deadline, the lowest assignment will be dropped. Grading will be handled by Aplia. You
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must access the Aplia website, which means you must register for an account at: http://www.aplia.com. Please register within 24 hours of the first class meeting.
The computer is unforgiving about accepting late assignments. Time is kept at Aplia, and not by the computer you are working on. You may appeal grading decisions made by the computer, if you can demonstrate that an error has been made.
Non-Aplia assignments must be turned in during class on the day they are due. Assignments turned in after this time but before the assignment is handed back may receive one-half credit. Assignments turned in after the hand-back can no longer be accepted for credit.
The worst thing some students do in a course is not think about course material a little every day. They sometimes let weeks go by and then try to learn all the material in one or two days. This usually does not work. Assignments will require keeping up-to-date. "Repetitio est mater studiorum." (Repetition is the mother of learning.)
Course Management Policies
Students are expected to be partners with the instructor in their educational experience. Frequent communication with the instructor is encouraged.
Attendance: You are expected to attend every class session. Attendance is not taken every day, but frequent absences will be noticed. Attendance is mandatory on days when quizzes are returned. Two absences on those days will reduce your letter grade.
Cheating: The search for truth and the dissemination of knowledge are the central missions of a university. Benedictine University pursues these missions in an environment guided by our Roman Catholic tradition and our Benedictine heritage. Integrity and honesty are therefore expected of all BU students. Actions such as cheating, plagiarism, collusion, solicitation, and misrepresentation are violations of these expectations and constitute unacceptable behavior in the University community.
To access the complete Academic Honesty Policy, which includes student responsibilities, responsibilities and authority of faculty, violations, reporting and communicating, responsibilities of the Provost, appeals, the academic appeals board, and records, please visit www.ben.edu/ahp. Penalties for cheating can range from a private verbal warning, all the way to expulsion from the University.
Incomplete Grade: A grade of “I” may be requested by a student for a course in which he or she is doing satisfactory work but, for illness or other circumstances beyond the student’s control, as determined by the instructor, the required work cannot be completed by the end of the semester. To qualify for the grade, a student must have satisfactory academic standing, be doing at least “C” work in the class, and submit a written request with a plan for completion approved by the instructor stating the reason for the delay in completing the work. Arrangements for the “I” grade must be made prior to the final examination. One may not receive an “I” in a semester in which he or she is already on academic probation. An “I” is a temporary grade. Failure to complete the course work and obtain a final grade within 180 days from the end of
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the term in which the “I” was received will result in the “I” immediately becoming an “F.”
Recommended Exercises: Students should work as many as possible of the even-numbered exercises in the text. Proficiency gained from practice on these will help when similar problems appear on quizzes. Answers to even-numbered exercises are at the back of the book.
Missed Quizzes: Make-up quizzes will be given only if a quiz was missed for a good and documented reason. If a make-up is given. The quiz score may be reduced 20% in an effort to maintain some degree of fairness to those who took the quiz at the proper time.
Student Responsibilities• Students who are not enrolled in class cannot attend the class and cannot receive
credit.• Students cannot submit additional work after grades have been submitted (except
in cases of temporary grades such as “I,” “X,” or “IP”).• Students on academic probation are not eligible for a grade of “I.”
Students are responsible for planning their academic programs and progress, and for evidencing academic performance with honesty and integrity (see “cheating” above). However, the University encourages students to assist one another (e.g. tutoring and group projects) and this course explicitly promotes such behavior.
Electronic Devices: One aspect of being a member of a community of scholars is to show respect for others by creating and maintaining an environment conducive to learning. To minimize distractions, electronic devices may be used only in connection with currently-discussed course material. Electronic devices used during a quiz, other than the approved TI calculator, will result in a zero grade for that quiz.
University Closings: A variety of conditions may disrupt scheduled classes—weather, building issues, health-related issues, etc. For severe weather, contact the BU emergency information line at(630) 829-6622 or check www.emergencyclosings.com or www.cancellations.com. Radio stations WBBM 780 AM and WGN 720 AM announce closings.
Faculty are required to provide students with alternate activities so that the learning process continues and the course objectives are met. Additional procedures may be implemented by the University in the event of an extended closing.
Technology Requirement: Students are expected to have basic skills in word processing and spreadsheet development, and effectively use technology to support oral presentations.
Access to the University computer network and to the University email system is gained through the use of login IDs. Each person’s Login ID is unique and access is controlled by a password of your choosing. For instructions on obtaining login IDs and email addresses, see http://www.ben.edu/ithome/faqs.asp.
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Recording (audio) Lectures: Audio recording is permitted with the instructor’s approval. University policy strictly prohibits video recording.
Special Needs and Americans with Disabilities ACT (ADA): If you have a documented learning, psychological, or physical disability, you may be eligible for reasonable academic accommodations or services. To request these, contact the Student Success Center. All students are expected to fulfill essential course or degree requirements.
Religious Accommodations: Students whose religious obligations conflict with a course requirement may request an accommodation from the instructor. Such requests must be made in writing by the end of the first week of class.
FERPA: The Family Education Rights and Privacy Act, also known as the Buckley Amendment, addresses the issue of student privacy. Enacted in 1974, guidelines were established prohibiting institutions from releasing information to anyone without expressed written permission from the student. This includes discussing student schedules, grades, or other specific information with spouses, family members, or friends.
A student may provide for release of identifiable, non-directory information to a third party by signing a Confidential Release Authorization form. For more information please see http://www.ben.edu/ferpa/index.cfm.
Mission Statement: Benedictine University dedicated itself to the education of undergraduate and graduate students from diverse ethnic, racial, and religious backgrounds. As an academic community committed to liberal arts and professional education, distinguished and guided by its Roman Catholic tradition and Benedictine heritage, the University prepares its students for a lifetime as active, informed, and responsible citizens and leaders in the world community.
Assignment Feedback Policy: The instructor will provide feedback on each graded assignment (quizzes, papers, homework, exams, etc.) no later than 10 calendar days after submission. Students are encouraged to review their individual course grades and to request clarification as needed. Quiz and homework scores, and class statistics, will be reviewed after each quiz. Final grades are issued only by the University Registrar.
Final comments: Feel free to see me if there is anything else of concern to you. Your comments about this course or any course are always welcome and appreciated. You are responsible for the information in the syllabus and should ask for clarification for anything in the syllabus about which you are unsure.
The remaining pages are (1) a detailed outline of each of the five parts of the course, including terminology, concepts, skills, and procedures, and (2) a statement of Course Philosophy.
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Essential Ideas, Terminology, Skills/Procedures, and Concepts for Each Part of the Course
Part I
Two Types of Statistics: Descriptive and InferentialDescriptive Statistics--purpose: to communicate characteristics of a set of data
Characteristics: Mean, median, mode, variance, standard deviation, skewness, etc.
Charts, graphsInferential Statistics--purpose: to make statements about population parameters
based on sample statisticsPopulation--group of interest being studied; often too large to sample every
memberSample--subset of the population; must be representative of the population
Random sampling is a popular way of obtaining a representative sample.Parameter--a characteristic of a population, usually unknown, often can be
estimated: Population mean, population variance, population proportion, etc.Statistic--a characteristic of a sample: Sample mean, sample variance, sample
proportion, etc.Two ways of conducting inferential statistics
EstimationPoint estimate--single number estimate of a population parameter, no
recognition of uncertainty, such as: "40" to estimate the average age of the voting population
Interval estimate--point estimate with an error factor, as in: "40 ± 5"The error factor provides formal and quantitative recognition of uncertainty.
Confidence level (confidence coefficient)--the probability that the parameter being estimated actually is in the stated range
Hypothesis testingNull hypothesis--an idea about an unknown population parameter, such as: "In
the population, there is no correlation between smoking and lung cancer."Alternate hypothesis--the opposite idea about the unknown population
parameter, such as: "In the population, there is correlation between smoking and lung cancer."
Data are gathered to see which hypothesis is supported. The result is either rejection or non-rejection (acceptance) of the null hypothesis.
Four types of dataNominal
Names, labels, categories (e.g. cat, dog, bird, rabbit, ferret, gerbil)Ordinal
Suggests order, but computations on the data are impossible or meaningless (e.g. Pets can be listed in order of popularity--1-cat, 2-dog, 3-bird, etc.--but the difference between cat and dog is not related to the difference between dog and bird.)
IntervalDifferences are meaningful, but they are not ratios. There is no natural zero point (e.g. clock time--the difference between noon and 1 p.m. is the same amount of time as the difference between 1 p.m. and 2 p.m. But 2 p.m. is not
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twice as late as 1 p.m. unless you define the starting point of time as noon, thereby creating a ratio scale)
RatioDifferences and ratios are both meaningful; there is a natural zero point. (e.g. Length--8 feet is twice as long as 4 feet, and 0 feet actually does mean no length at all.)
Two types of statistical studiesObservational study (naturalistic observation)
Researcher cannot control the variables under study; they must be taken as they are found (e.g. most research in astronomy).
ExperimentResearcher can manipulate the variables under study (e.g. drug dosage).
Characteristics of DataCentral tendency--attempt to find a "representative" or "typical" value
Mean--the sum of the data items divided by the number of items, or Σx / nMore sensitive to outliers than the median
Outlier--data item far from the typical data itemMedian--the middle item when the items are ordered high-to-low or low-to-high
Also called the 50th percentileLess sensitive to outliers than the mean
Mode--most-frequently-occurring item in a data setDispersion (variation or variability)--the opposite of consistency
Variance--the Mean of the Squared Deviations (MSD), or Σ(x-xbar)2/nDeviation--difference between a data item and the mean
The sum of the deviations in any data set is always equal to zero.Standard Deviation--square root of the varianceRange--difference between the highest and lowest value in a data setCoefficient of Variation—measures relative dispersion
CV = standard deviation / meanSkewness--the opposite of symmetry
Positive skewness--mean exceeds median, high outliersNegative skewness--mean less than median, low outliersSymmetry--mean, median, mode, and midrange about the same
Kurtosis--degree of relative concentration or peakednessLeptokurtic--distribution strongly peakedMesokurtic--distribution moderately peakedPlatykurtic--distribution weakly peaked
Symbols & "Formula Sheet No. 1"Descriptive statistics
Sample Mean--"xbar" (x with a bar above it)Sample Variance--"svar" (the same as MSD for the sample)
Also, the "mean of the squares less the square of the mean"Sample Standard Deviation--"ssd"--square root of svar
Population parameters (usually unknown, but can be estimated)Population Mean--"μ" (mu)
Population Variance--"σ2" (sigma squared) (MSD for the population)Population Standard Deviation--"σ" (sigma)--square root of σ2
Inferential statistics--estimating of population parameters based on sample statistics
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Estimated Population Mean--"μ^" (mu hat)The sample mean is an unbiased estimator of the population mean.
Unbiased estimator--just as likely to be greater than as less than the parameter being estimatedIf every possible sample of size n is selected from a population, as many
sample means will be above as will be below the population mean.Estimated Population Variance--"σ^2" (sigma hat squared)
The sample variance is a biased estimator of the population variance.Biased estimator--not just as likely to be greater than as less than the
parameter being estimatedIf every possible sample of size n is selected from a population, more of the
sample variances will be below than will be above the population variance.The reason for this bias is the probable absence of outliers in the sample.
The variance is greatly affected by outliers.The smaller a sample is, the less likely it is to contain outliers, and hence
the lower its variance is likely to be.Note how the correction factor's [n / (n-1)] impact increases as the sample size
decreases.This quantity is also widely referred to as "s2" and is widely referred to as the
"sample variance."In this context "sample variance" does not mean variance of the sample; it
is, rather, a shortening of the cumbersome phrase "estimate of population variance computed from a sample."
Estimated Population Standard Deviation--"σ^" (sigma hat)--square root of σ^2
The bias considerations that apply to the estimated population variance also apply to the estimated population standard deviation.
This quantity is also widely referred to as "s", and is widely referred to as the "sample standard deviation."
In this context "sample standard deviation" does not mean standard deviation of the sample; it is, rather, a shortening of the cumbersome phrase "estimate of population standard deviation computed from a sample."
Calculator note--some calculators, notably TI's, compute two standard deviationsThe smaller of the two is the one we call "ssd"
TI calculator manuals call this the "population standard deviation."This refers to the special case in which the entire population is included in
the sample; then the sample standard deviation (ssd) and the population standard deviation are the same. (This also applies to means and variances.) There is no need for inferential statistics in such cases.
The larger of the two is the one we call σ^ (sigma-hat) (estimated population standard deviation).TI calculator manuals call this the "sample standard deviation."
This refers to the more common case in which "sample standard deviation" really means estimated population standard deviation, computed from a sample.
Significance of the Standard DeviationNormal distribution (empirical rule)--empirical: derived from experience
Two major characteristics: symmetry and center concentrationTwo parameters: mean and standard deviation
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"Parameter," in this context, means a defining characteristic of a distribution. Mean and median are identical (due to symmetry) and are at the high point.Standard deviation--distance from mean to inflection point
Inflection point--the point where the second derivative of the normal curve is equal to zero,
or, the point where the curvature changes from "right" to "left" (or vice-versa), as when
you momentarily travel straight on an S-curve on the highway z-value--distance from mean, measured in standard deviationsAreas under the normal curve can be computed using integral calculus.
Total area under the curve is taken to be 1.000 or 100%Tables enable easy determination of these areas.
about 68-1/4%, 95-1/2%, and 99-3/4% of the area under a normal curve lie within one, two, and three standard deviations from the mean, respectively
Many natural and economic phenomena are normally distributed.Tchebyshev's Theorem (or Chebysheff P. F., 1821-1894)
What if a distribution is not normal? Can any statements be made as to what percentage of the area lies within various distances (z-values) of the mean?
Tchebysheff proved that certain minimum percentages of the area must lie within various z-values of the mean.The minimum percentage for a given z-value, stated as a fraction,
is [ (z2-1) / z2 ]Tchebysheff's Theorem is valid for all distributions.
Other measures of relative standingPercentiles--A percentile is the percentage of a data set that is below a specified
value.Percentile values divide a data set into 100 parts, each with the same number of
items.The median is the 50th percentile value.
Z-values can be converted into percentiles and vice-versa.A z-value of +1.00, for example, corresponds to the 84.13 percentile.The 95th percentile, for example, corresponds to a z-value of +1.645.A z-value of 0.00 is the 50th percentile, the median.
DecilesDecile values divide a data set into 10 parts, each with the same number of items.The median is the 5th decile value.The 9th decile value, for example, separates the upper 10% of the data set from
the lower 90%. (Some would call this the 1st decile value.)Quartiles
Quartile values divide a data set into 4 parts, each with the same number of items.The median is the 2nd quartile value.The 3rd quartile value (Q3), for example, separates the upper 25% of the data set
from the lower 75%.Q3 is the median of the upper half; Q1 (lower quartile) is the median of the lower half
Other possibilities: quintiles (5 parts), stanines (9 parts)Some ambiguity in usage exists, especially regarding quartiles--For example, the
phrase "first quartile" could mean one of two things: (1) It could refer to the value
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that separates the lower 25% of the data set from the upper 75%, or (2) It could refer to the members, as a group, of the lower 25% of the data.
Example (1): "The first quartile score on this test was 60."Example (2): "Your score was 55, putting you in the first quartile."
Also the phrase "first quartile" is used by some to mean the 25th percentile value, and by others to mean the 75th percentile value. To avoid this ambiguity, the phrases "lower quartile," "middle quartile," and "upper quartile" may be used.
TerminologyStatistics, population, sample, parameter, statistic, qualitative data, quantitative data, discrete data, continuous data, nominal measurements, ordinal measurements, interval measurements, ratio measurements, observational study (naturalistic observation), experiment, precision, accuracy, sampling, random sampling, stratified sampling, systematic sampling, cluster sampling, convenience sampling, representativeness, inferential statistics, descriptive statistics, estimation, point estimation, interval estimation, hypothesis testing, dependency, central tendency, dispersion, skewness, kurtosis, leptokurtic, mesokurtic, platykurtic, frequency table, mutually exclusive, collectively exhaustive, relative frequencies, cumulative frequency, histogram, Pareto chart, bell-shaped distribution, uniform distribution, skewed distribution, pie chart, pictogram, mean, median, mode, bimodal, midrange, reliability, symmetry, skewness, positive skewness, negative skewness, range, MSD, variance, deviation, standard deviation, z-value, Chebyshev's theorem, empirical rule, normal distribution, quartiles, quintiles, deciles, percentiles, interquartile range, stem-and-leaf plot, boxplot, biased, unbiased.
Skills/Procedures--given appropriate data, compute or identify theSample mean, median, mode, variance, standard deviation, and rangeEstimated population mean, variance, and standard deviationKind of skewness, if any, present in the data setz-value of any data itemUpper, middle, and lower quartilesPercentile of any data itemPercentile of any integer z-value from -3 to +3
ConceptsIdentify circumstances under which the median is a more suitable measure of central
tendency than the meanExplain when the normal distribution (empirical rule) may be usedExplain when Chebyshev's Theorem may be used; when it should be usedGive an example (create a data set) in which the mode fails as a measure of central
tendencyGive an example (create a data set) in which the mean fails as a measure of central
tendencyExplain why the sum of the deviations fails as a measure of dispersion, and describe
how this failure is overcomeDistinguish between unbiased and biased estimators of population parametersDescribe how percentile scores are determined on standardized tests like the SAT or
the ACT
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Explain why the variance and standard deviation of a sample are likely to be lower than the variance and standard deviation of the population from which the sample was taken
Identify when the sample mean, variance, and standard deviation are identical to the population mean, variance, and standard deviation
Part II
Basic Probability Concepts
Probability--the likelihood of an eventProbability is expressed as a decimal or fraction between zero and one, inclusive.
An event that is certain has a probability of 1.An event that is impossible has a probability of 0.If the probability of rain today (R) is 30%, it can be written P(R) = 0.3.
Objective probabilities--calculated from data according to generally-accepted methodsRelative frequency method--example: In a class of 25 college students there are
14 seniors. If a student is selected at random from the class, the probability of selecting a
senior is 14/25 or 0.56. Relative to the number in the class, 25, the number of seniors (frequency), 14, is 56% or 0.56.
Subjective probabilities--arrived at through judgment, experience, estimation, educated guessing, intuition, etc. There may be as many different results as there are people making the estimate. (With objective probability, all should get the same answer.)
Boolean operations--Boolean algebra--(George Boole, 1815-1864)Used to express various logical relationships; taught as "symbolic logic" in college
philosophy and mathematics departments; important in computer designComplementation--translated by the word "not"--symbol: A¯or A-bar
Complementary events are commonly known as "opposites."Examples: Heads/Tails on a coin-flip; Rain/No Rain on a particular day; On
Time/Late for workComplementary events have two properties
Mutually exclusive--they cannot occur together; each excludes the otherCollectively exhaustive--there are no other outcomes; the two events are a complete or exhaustive list of the possibilities
Partition--a set of more than two events that are mutually exclusive and collectively exhaustive
Examples: A, B, C, D, F, W, I--grades received at the end of a course; Freshman, Sophomore, Junior, Senior--traditional college student categories
The sum of the probabilities of complementary events, or of the probabilities of all the events in a partition, is 1.
Intersection--translated by the words "and," "with," or "but"--symbol: or, for typing convenience, n
A day that is cool (C) and rainy (R) can be designated (CnR).If there is a 25% chance that today will be cool (C) and rainy (R), it can be
written P(CnR) = 0.25.Intersections are often expressed without using the word "and."
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Examples: "Today might be cool with rain." or "It may be a cool, rainy day."Two formulas for intersections:
For any two events A and B: P(AnB) = P(A|B)*P(B) ("|" is defined below.)For independent events A and B: P(AnB) = P(A)*P(B)
This can be used as a test for independence.This formula may be extended to any number of independent events
P(AnBnCn . . . nZ) = P(A)*P(B)*P(C)* . . . P(Z)The intersection operation has the commutative property
P(AnB) = P(BnA)"Commutative" is related to the word "commute" which means "to switch."The events can be switched without changing anything.In our familiar algebra, addition and multiplication are commutative, but
subtraction and division are not.Intersections are also called "joint (together) probabilities."
Union--translated by the word "or"--symbol: or, for typing convenience, uA day that is cool (C) or rainy (R) can be designated (CuR).
If there is a 25% chance that today will be cool (C) or rainy (R), it can be written P(CuR) = 0.25.
Unions always use the word "or."Addition rule to compute unions: P(AuB) = P(A) + P(B) – P(AnB)
The deduction of P(AnB) eliminates the double counting of the intersection that occurs when P(A) is added to P(B).
The union operation is commutative: P(AuB) = P(BuA)Condition--translated by the word "given"--symbol: |
A day that is cool (C) given that it is rainy (R) can be designated (C|R). The event R is called the condition.
If there is a 25% chance that today will be cool (C) given that it is rainy (R), it can be written P(C|R) = 0.25.
Conditions are often expressed without using the word "given."Examples: "The probability that it will be cool when it is rainy is 0.25."
P(C|R) = 0.25."The probability that it will be cool if it is rainy is 0.25." P(C|R) = 0.25."25% of the rainy days are cool." [P(C|R) = 0.25.]
All three of the above statements are the same, but the next one is different:"25% of the cool days are rainy." This one is P(R|C) = 0.25.
The condition operation is not commutative: P(A|B) ≠ P(B|A)For example, it is easy to see that P(rain|clouds) is not the same as P(clouds|rain).
Conditional probability formula: P(A|B) = P(AnB) / P(B)
Occurrence Tables and Probability TablesOccurrence table--table that shows the number of items in each category and
in the intersections of categoriesCan be used to help compute probabilities of single events,
intersections, unions, and conditional probabilitiesProbability table--created by dividing every entry in an occurrence table
by the total number of occurrences.Probability tables contain marginal probabilities and joint probabilities.
Marginal probabilities--probabilities of single events, found in the right and bottom margins of the table
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Joint probabilities--probabilities of intersections, found in the interior part of the table where the rows and columns intersect
Unions and conditional probabilities are not found directly in a probability table, but they can be computed easily from values in the table.
Two conditional probabilities are complementary if they have the same condition and the events before the "bar" (|) are complementary. For example, if warm (W) is the opposite of cool, then (W|R) is the complement of (C|R),
and P(W|R) + P(C|R) = 1. In a 2 x 2 probability table, there are eight conditional probabilities, forming four
pairs of complementary conditional probabilities.It is also possible for a set of conditional probabilities to constitute a partition
(if they all have the same condition, and the events before the "bar" are a partition).
Testing for Dependence/IndependenceStatistical dependence
Events are statistically dependent if the occurrence of one event affects the probability of the other event.
Identifying dependencies is one of the most important tasks of statistical analysis.Tests for independence/dependence
Conditional probability test--posterior/prior testPrior and posterior are the Latin words for "before" and "after."A prior probability is one that is computed or estimated before additional
information is obtained.A posterior probability is one that is computed or estimated after additional information is obtained.Prior probabilities are probabilities of single events, such as P(A).Posterior probabilities are conditional probabilities, such as P(A|B).Independence exists between any two events A and B if P(A|B) = P(A)
If P(A|B) = P(A), the occurrence of B has no effect on P(A)If P(A|B) ≠ P(A), the occurrence of B does have an effect on P(A)
Positive dependence if P(A|B) > P(A) -- posterior greater than priorNegative dependence if P(A|B) < P(A) -- posterior less than prior
Multiplicative test--joint/marginal testIndependence exists between any two events A and B if P(AnB) = P(A)*P(B)
Positive dependence if P(AnB) > P(A)*P(B) -- intersection greater than the product
Negative dependence if P(AnB) < P(A)*P(B) -- intersection less than the product
Bayesian Inference--Thomas Bayes (1702-1761)Bayes developed a technique to compute a conditional probability,
given the reverse conditional probabilityComputations are simplified, and complex formulas can often be avoided, if a
probability table is used.Basic computation is: P(A|B) = P(AnB) / P(B), an intersection probability divided by
a single-event probability. That is, a joint probability divided by a marginal probability.Bayesian analysis is very important because most of the probabilities upon which we
base decisions are conditional probabilities.
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Other Probability Topics:Matching-birthday problem
Example of a "sequential" intersection probability computation, where each probability is revised slightly and complementary thinking is used
Complementary thinking--strategy of computing the complement (because it is easier) of what is really needed, then subtracting from 1
RedundancyStrategy of using back-ups to increase the probability of successUsually employs complementary thinking and the extended multiplicative rule for
independent events to compute the probability of failure. P(Success) is then equal to 1 – P(Failure).
Permutations and CombinationsPermutation--a set of items in which the order is important
Without replacement--duplicate items are not permittedWith replacement--duplicate items are permitted
Combination--a set of items in which the order is not importantWithout replacement--duplicate items are not permittedWith replacement--duplicate items are permitted
In the formulas, "n" designates the number of items available, from which "r" is the number that will be chosen. (Can r ever exceed n?)
To apply the correct formula when confronting a problem, two decisions must be made: Is order important or not? Are duplicates permitted or not?
Permutations, both with and without replacement, can be computed by using the "sequential" method instead of the formula. This provides way of verifying the formula result.
LotteriesUsually combination ("Lotto") or permutation ("Pick 3 or 4") problemsLotto games are usually without replacement--duplicate numbers are not possiblePick 3 or 4 games are usually with replacement--duplicate numbers are possible
Poker handsCan be computed using combinations and the relative frequency methodCan also be computed sequentially
Terminology PROBABILITY:
probability, experiment, event, simple event, compound event, sample space, relative frequency method, classical approach, law of large numbers, random sample, impossible event probability, certain event probability, complement, partition, subjective probability, occurrence table, probability table, addition rule for unions, mutually exclusive, collectively exhaustive, redundancy, multiplicative rule for intersections, tree diagram, statistical independence/dependence, conditional probability, Bayes' theorem, acceptance sampling, simulation, risk assessment, redundancy, Boolean algebra, complementation, intersection, union, condition, marginal probabilities, joint probabilities, prior probabilities, posterior probabilities, two tests for independence, triad, complementary thinking, commutative. PERMUTATIONS AND COMBINATIONS:
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permutations, permutations with replacement, sequential method, combinations, combinations with replacement.
Skills/Procedures--given appropriate data, prepare an occurrence tablePROBABILITYprepare a probability tablecompute the following 20 probabilities
4 marginal probabilities (single simple events)4 joint probabilities (intersections)4 unions8 conditional probabilities--identify the 4 pairs of conditional complementary
eventsidentify triads (one unconditional and two conditional probabilities in each triad)conduct the conditional (prior/posterior) probability test for independence /
dependenceconduct the multiplication (multiplicative) (joint/marginal) test for independence /
dependenceidentify positive / negative dependencyidentify Bayesian questionsuse the extended multiplicative rule to compute probabilitiesuse complementary thinking to compute probabilitiescompute the probability of "success" when redundancy is usedcompute permutations and combinations with and without replacement
ConceptsPROBABILITYgive an example of two or more events that are not mutually exclusivegive an example of two or more events that are not collectively exhaustivegive an example of a partition--a set of three or more events that are mutually
exclusive and collectively exhaustiveexpress the following in symbolic form using F for females and V for voters in a
retirement community60% of the residents are females30% of the residents are female voters50% of the females are voters75% of the voters are female70% of the residents are female or voters30% of the residents are male non-voters25% of the voters are male40% of the residents are male
identify which two of the items above are a pair of complementary probabilitiesidentify which two of the items above are a pair of complementary conditional
probabilitiesfrom the items above, comment on the dependency relationship between F and Vif there are 100 residents, determine how many female voters there would be if
gender and voting were independentexplain why joint probabilities are called "intersections"?identify which two of our familiar arithmetic operations and which two Boolean
operations are commutative
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tell what Thomas Bayes is known for (not English muffins)
PERMUTATIONS AND COMBINATIONS:give an example of a set of items that is a permutationgive an example of a set of items that is a combination tell if, in combinations/permutations, "r" can ever exceed "n" give an example
Part III
Permutations and Combinations (outline, etc. Repeated from Part II)Permutation--a set of items in which the order is important
Without replacement--duplicate items are not permittedWith replacement--duplicate items are permitted
Combination--a set of items in which the order is not importantWithout replacement--duplicate items are not permittedWith replacement--duplicate items are permitted
In the formulas, "n" designates the number of items available, from which "r" is the number that will be chosen. (Can r ever exceed n?)
To apply the correct formula when confronting a problem, two decisions must be made: Is order important or not? Are duplicates permitted or not?
Permutations, both with and without replacement, can be computed by using the "sequential" method instead of the formula. This provides way of verifying the
formula result.
LotteriesUsually combination ("Lotto") or permutation ("Pick 3 or 4") problemsLotto games are usually without replacement--duplicate numbers are not possiblePick 3 or 4 games are usually with replacement--duplicate numbers are possible
Poker handsCan be computed using combinations and the relative frequency methodCan also be computed sequentially
Terminology PERMUTATIONS AND COMBINATIONS:
permutations, permutations with replacement, sequential method, combinations, combinations with replacement.
Skills/Procedures--given appropriate data, PERMUTATIONS AND COMBINATIONS:decide when order is and is not importantdecide when selection is done with replacement and without replacementcompute permutations with and without replacement using the permutation formulacompute combinations wi2th and without replacement using the combination
formulause the sequential method to compute permutations with and without replacementsolve various applications problems involving permutations and combinations
give an example of a set of items that is a permutation
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give an example of a set of items that is a combination tell if, in combinations/permutations,
"r" can ever exceed "n"
Mathematical ExpectationDiscrete variable--one that can assume only certain values (often the whole numbers)
There is only a finite countable number of values between any two specified values.
Examples: the number of people in a room, your score on a quiz in this course, shoe sizes (certain fractions permitted), hat sizes (certain fractions permitted)
Continuous variable--one that can take on any value--there is an infinite number of values between any two specified valuesExamples: your weight (can be any value, and changes as you breathe), the
length of an object, the amount of time that passes between two events, the amount of water in a container (but if you look at the water closely enough, you find that it is made up of very tiny chunks--molecules--so this last example is really discrete at the submicroscopic level, but in ordinary everyday terms we would call it continuous)
Mean (expected value) of a discrete probability distributionProbability distribution--a set of outcomes and their likelihoodsMean is the probability-weighted average of the outcomes
Each outcome is multiplied by its probability, and these are added.The result is not an estimate. It is the actual population value, because the
probability distribution specifies an entire population of outcomes. ("μ" may be used, without the estimation caret above it.)
The mean need not be a possible outcome, and for this reason the term "expected value" can be misleading.
Variance of a discrete probability distributionVariance is the probability-weighted average of the squared deviations
similar to MSD, except it's a weighted averageEach squared deviation is multiplied by its probability, and these are added.The result is not an estimate. It is the actual population value, because the
probability distribution specifies an entire population of outcomes. ("σ2" may be used, without the estimation caret above it.)
Standard deviation of a discrete probability distribution--the square root of the variance
("σ" may be used, without the estimation caret ^ above it.)
The Binomial DistributionBinomial experiment requirements
Two possible outcomes on each trialThe two outcomes are (often inappropriately) referred to as "success" and
"failure."n identical trialsIndependence from trial to trial--the outcome of one trial does not affect the
outcome of any other trialConstant p and q from trial to trial
p is the probability of the "success" event q is the probability of the "failure" event; (q = (1-p) )
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"x" is the number of "successes" out of the n trials.Symmetry is present when p = q
When p < .5, the distribution is positively skewed (high outliers).When p > .5, the distribution is negatively skewed (low outliers).
Binomial formula--for noncumulative probabilitiesCumulative binomial probabilities--computed by adding the noncumulative probabilities
Binomial probability tables--may show cumulative or noncumulative probabilitiesIf cumulative, compute noncumulative probabilities by subtraction
Parameters of the binomial distribution--n and pBinomial formula: P(x) = n!/(x!(n-x)! * p^x * q^(n-x)
Note that when x=n, the formula reduces to p^n, and when x=0, the formula reduces to q^n.
These are just applications of the multiplicative rule for independent events.
The Normal DistributionNormal distribution characteristics--center concentration and symmetryParameters of the normal distribution--μ (mu), mean; and σ (sigma), standard
deviationZ-value formula (four arrangements--for z, x, μ, and σ)
Normal distribution problems have three variables given, and the fourth must becomputed and interpreted.
Z-values determine areas (probabilities) and areas (probabilities) determine z-values--the normal
table or calculators converts from one to the other.Normal distribution probability tables--our text table presents one-sided central
areasTwo uses of the normal distribution
Normally-distributed phenomenaTo approximate the binomial distribution--this application is far less important
now that computers and calculators can generate binomial probabilitiesBinomial parameters (n and p) can be converted to normal parameters μ and σ
μ = np; σ2 = (npq); σ = (npq)
TerminologyMATHEMATICAL EXPECTATION: random variable, discrete variable, continuous variable,
probability distribution, probability histogram, mean of a probability distribution, variance and standard deviation of a probability distribution, probability-weighted average of outcomes (mean), probability-weighted average of squared deviations (variance).
BINOMIAL DISTRIBUTION: binomial experiment, requirements for a binomial experiment, independent trials, binomial probabilities, cumulative binomial probabilities, binomial distribution symmetry conditions, binomial distribution skewness conditions, binomial distribution parameters, mean and variance of a binomial distribution
NORMAL DISTRIBUTIONnormal distribution, normal distribution parameters, mean, standard deviation, standard normal distribution, z-value, reliability, validity
Skills/ProceduresMATHEMATICAL EXPECTATION:
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compute the mean, variance, and standard deviation of a discrete random variablesolve various applications problems involving discrete probability distributions
BINOMIAL DISTRIBUTION:compute binomial probabilities and verify results with table in textbookcompute cumulative binomial probabilitiescompute binomial probabilities with p = q and verify symmetrysolve various application problems using the binomial distribution
NORMAL DISTRIBUTION -- given appropriate data, determine a normal probability (area), given x, μ, and σdetermine x, given μ, σ, and the normal probability (area)determine μ, given x, σ, and the normal probability (area)determine σ, given x, μ, and the normal probability (area)solve various applications problems involving the normal distributioncompute the sampling standard deviation (standard error) from the population
standard deviation and the sample sizesolve various applications problems involving the central limit theorem
ConceptsMATHEMATICAL EXPECTATION
give an example (other than water) of something that looks continuous at a distance, but, when you get up close, turns out to be discrete
explain why "expected value" may be a misleading name for the mean of aprobability distribution
describe how to compute a weighted averageBINOMIAL DISTRIBUTION:
explain why rolling a die is or is not a binomial experimentexplain why drawing red/black cards from a deck of 52 without replacement is or is
not a binomial experimentexplain why drawing red/black cards from a deck of 52 with replacement is or is not
a binomial experimentNORMAL DISTRIBUTION
describe conditions under which the normal distribution is symmetricdescribe the kind of shift in the graph of a normal distribution caused by a change in
the meandescribe the kind of shift in the graph of a normal distribution caused by a change in
the standard deviationexplain why, as the sample size increases, the distribution of sample means clusters
more and more closely around the population mean
Part IV
Sampling DistributionsSampling distribution of the mean--the distribution of the means of many samples of
the same size drawn from the same populationCentral Limit Theorem--three statements about the sampling distribution of sample means:
1. Sampling distribution of the means is normal in shape, regardless of the population distribution shape when the sample size, n, is large. (When n is
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small, the population must be normal in order for the sampling distribution of the mean to be normal.) ("Large" n is usually taken to be 30 or more.)2. Sampling distribution of the means is centered at the true population mean.3. Sampling distribution of the means has a standard deviation equal to σ / n.
This quantity is called the sampling standard deviation or the standard error (of the mean).(The full name is "standard deviation of the sampling distribution of the mean(s).”) This quantity is represented by the symbol σx bar.
σx bar is less than σ because of the offsetting that occurs within the sample. The largerthe sample size n, the smaller the σx bar (standard error), because the larger the
n, the greater the amount of offsetting that can occur, and the sample means will cluster more closely around the true population mean μ.
Sampling standard deviation (σx bar or standard error)--key value for inferential statisticsTwo uses of the standard error
Computing the error factor in interval estimationComputing the test statistic (zc or tc) in hypothesis testing
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Terminologynormal distribution, normal distribution parameters, mean, standard deviation, standard normal distribution, z-value, reliability, validity, sampling distribution, central limit theorem (three parts), sampling standard deviation, standard error, offsetting, effect of the sample size on the sampling standard deviation (standard error).
Skills/Procedures--given appropriate data, determine a normal probability (area), given x, μ, and σdetermine x, given μ, σ, and the normal probability (area)determine μ, given x, σ, and the normal probability (area)determine σ, given x, μ, and the normal probability (area)solve various applications problems involving the normal distributioncompute the sampling standard deviation (standard error) from the population
standard deviation and the sample sizesolve various applications problems involving the central limit theorem
Concepts--describe conditions under which the normal distribution is symmetricdescribe the kind of shift in the graph of a normal distribution caused by a change in
the meandescribe the kind of shift in the graph of a normal distribution caused by a change in
the standard deviationexplain why, as the sample size increases, the distribution of sample means clusters
more and more closely around the population mean
Part V
Interval Estimation--Large SamplesFour Types of Problems
Means--one-group; two-groupColumns one and two of the four-column formula sheet
Proportions--one-group; two-groupColumns three and four of the four-column formula sheet
Confidence level (confidence coefficient)--the probability that a confidence interval will actually contain the population parameter being estimated (confidence interval is a
range of values that is likely to contain the population parameter being estimated).
90%, 95%, and 99% are the most popular confidence levels, and correspond to z-values of 1.645, 1.960, and 2.576, respectively.Of these, 95% is the most popular, and is assumed unless another value is
mentioned.Error (uncertainty) factors express precision, as in 40 ± 3.
Upper confidence limit--the point estimate plus the error factor, 43 in this exampleLower confidence limit--the point estimate minus the error factor, 37 in this exampleError factor is the product of the z-value and the standard error: zt * σx bar.
Required sample sizes for desired precision may be computed.Increased precision means a lower error factor.Precision can be increased by increasing the sample size, n.
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Increasing n lowers the standard error, since the standard error = σ / n.Taken to the extreme, every member of the population may be sampled, in
which case the error factor becomes zero--no uncertainty at all--and the population parameter is found exactly.
Economic considerations--the high cost of precisionThe required increase in n is equal to the square of the desired increase in
precision.To double the precision--to cut the error factor in half--the sample size must be
quadrupled. Doubling the precision may thus quadruple the cost.To triple the precision--to cut the error factor to 1/3 of its previous value, n must be
multiplied by 9.
Hypothesis Testing--Large SamplesFour Types of Problems--Four-column formula sheet
Means--one-group; two-groupProportions--one-group; two-group
Null (Ho) and alternate (Ha) hypothesesMeans, one-group
H0: μ = some valueHa: μ ≠ that same value (two-sided test)
μ > that same value (one-sided test, high end, right side)μ < that same value (one-sided test, low end, left side)
Means, two-groupH0: μ1 = μ2Ha : μ1 ≠ μ2 (two-sided test)
μ1 > μ2 (one-sided test, high end, right side)μ1 < μ2 (one-sided test, low end, left side)
Proportions, one-groupH0: π = some valueHa : π ≠ that same value (two-sided test)
π > that same value (one-sided test, high end, right side)π < that same value (one-sided test, low end, left side)
Proportions, two-groupH0: π1 = π2Ha : π1 ≠ π2 (two-sided test)
π1 > π2 (one-sided test, high end, right side)π1 < π2 (one-sided test, low end, left side)
Type I errorErroneous rejection of a true H0
Probability of a Type I error is symbolized by α (alpha)Type II error
Erroneous acceptance of a false H0Probability of a Type II error is symbolized by β (beta)
Selecting α--based on researcher’s attitude toward riskα--the researcher's maximum tolerable risk of committing a type I error0.10, 0.05, and 0.01 are the most commonly used.
Of these, 0.05 is the most common--known as "the normal scientific standardof proof."
Table-z (critical value); symbolized by zt; determined by the selected α value α 2-sided z 1-sided z
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0.10 1.645 1.2820.05 1.960 1.6450.01 2.576 2.326
Calculated-z (test statistic); symbolized by zcFraction--"signal-to-noise" ratio
Numerator ("signal")--strength of the evidence against H0Denominator ("noise")--uncertainty factor for the numerator
Rejection criteriaTwo-sided test: |zc| >= |zt|; also p <= αOne-sided test: |zc| >= |zt|, AND zc and zt have the same sign; also p <= α
Significance level (p-value) ("p" stands for probability)Actual risk (probability) of a Type I error if H0 is rejected on the basis of the
experimental evidenceGraphically, the area beyond the calculated z-value, zc.
Treatment--in a column-2 test, the difference that the experimenter introduces between the two groups
Terminologyinferential statistics, sample mean, population mean, estimator, estimate, unbiased estimator, point estimate, interval estimate, confidence interval, degree of confidence, confidence level, table-z, error factor, required sample size, upper confidence limit, lower confidence limit, hypothesis test, null hypothesis, alternate hypothesis, type I error, α, type II error, β, calculated-z (test statistic), critical region, table-z (critical value of z), rejection of the null hypothesis, non-rejection of the null hypothesis, p-value, hypothesis-test conclusion, independent samples, standard error of the difference, sample proportion, population proportion, pooled proportion (two-group proportion cases), treatment
Skills/Procedures• given appropriate data, conduct estimation and hypothesis testing on the population mean of one group (col. 1), using these ten steps:
1. make a point estimate of a population mean2. compute the sampling standard deviation (standard error) of the sample
means3. compute and interpret the error factor for the interval estimate for the 90%,
95%, and 99% confidence levels4. determine the sample size needed to obtain a given desired error factor5. state the null and alternate hypotheses regarding the population mean6. determine the table-z (critical value of z) for alpha levels of 0.10, 0.05 and
0.017. compute the calculated-z (test statistic)8. draw the appropriate hypothesis-test conclusion based on the given level of α,
the table-z (critical value) and the calculated-z (test statistic)9. interpret the conclusion
10. determine and interpret the p-value
• given appropriate data, conduct estimation and hypothesis testing on the population means of two groups (col. 2), using these ten steps:
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1. make a point estimate of the difference between population means 2. compute the sampling standard deviation (standard error) of the difference
between sample means3. compute and interpret the error factor for the interval estimate for the 90%,
95% and 99% confidence levels4. determine the sample size needed to obtain a given desired error factor5. state the null and alternate hypotheses regarding the difference between
population means6. determine the table-z (critical value of z) for alpha levels of 0.10, 0.05 and
0.017. compute the calculated-z (test statistic)8. draw the appropriate hypothesis-test conclusion based on the given level of α,
the table-z, and the calculated-z9. interpret the conclusion
10 determine and interpret the p-value
• given appropriate data, conduct estimation and hypothesis testing on the population proportion of one group (col. 3), using these ten steps:1. make a point estimate of a population proportion2. compute the sampling standard deviation (standard error) of the sample
proportions3. compute and interpret the error factor for the interval estimate for the 90%,
95% and 99% confidence levels4. determine the sample size needed to obtain a given desired error factor5. state the null and alternate hypotheses regarding the population proportion6. determine the table-z (critical value of z) for alpha levels of 0.10, 0.05 and 0.017. compute the calculated-z (test statistic)8. draw the appropriate hypothesis-test conclusion based on the given level of α,
the table-z and the calculated-z9. interpret the conclusion
10. determine and interpret the p-value
• given appropriate data, conduct estimation and hypothesis testing on the population proportions of two groups (col. 4), involving these ten steps:
1. make a point estimate of the difference between population proportions2. compute the sampling standard deviation (standard error) of the difference
between sample proportions3. compute and interpret the error factor for the interval estimate for the 90%,
95% and 99% confidence levels4. determine the sample size needed to obtain a given desired error factor5. state the null and alternate hypotheses regarding the difference between
population proportions6. determine the table-z (critical value of z) for alpha levels of 0.10, 0.05 and 0.017. compute the calculated-z (test statistic)8. draw the appropriate hypothesis-test conclusion based on the given level of α,
the table-z and the calculated-z9. interpret the conclusion
10. determine and interpret the p-value
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Concepts--explain why a confidence interval becomes larger as the confidence level increasesexplain why a confidence interval becomes smaller as the sample size increasesdescribe the nature of the trade-off between precision and costidentify the type of error that is made if the null hypothesis is "the defendant is
innocent," and an innocent defendant is erroneously convictedidentify the type of error that is made if the null hypothesis is "the defendant is
innocent," and a guilty defendant is erroneously acquittedexplain why a researcher seeking to reject a null hypothesis may tend to prefer a
one-sided alternative hypothesis
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COURSE PHILOSOPHY -- STATISTICS
In an article in the Chronicle of Higher Education, Sharon Rubin, assistant dean at the University of Maryland, states that all course syllabi, in addition to providing the basic information on texts, topics, schedule, etc., should answer certain questions. The instructor of this course would like to share these questions with you, and provide some answers.
You are what you know. You are what you can do. "What value can you add to our organization?"
1. WHY SHOULD A STUDENT WANT TO TAKE THIS COURSE?
As a decision-maker, you must learn how to analyze and interpret quantitative information. Such skills will improve your ability to adopt the questioning attitude and independence of thought that are essential to leadership and success in any field. You may also have the opportunity to introduce statistical data analyses in areas where they are not currently in use, thus improving the quality of your organization's decisions.
2. WHAT IS THE RELEVANCE OF THIS COURSE TO THE DISCIPLINE?
Statistics courses are part of the curriculum in many of BU's programs. But since this course is part of a program leading to a degree in business, let us interpret the word "discipline" in this question to mean "management." This can refer to marketing management, financial management, human resource management, etc., even the management of your personal affairs. To MANAGE something requires the ability to exert some CONTROL over it, and the ability to exert control requires identification of DEPENDENCIES. In order to manage sales performance, for example, you must find things upon which sales depends (e.g. advertising budget; product price; number, training, and compensation of salespersons; interest rates; and competitive factors), and learn something about the nature of the dependencies. Statistics is the major tool for identifying dependencies.
Another example of the importance of identifying dependencies: a new disease appears. Researchers immediately try to find things that enhance the occurrence rate or the severity of the illness (positive dependencies), and things that reduce them (negative dependencies). Only after such things are found can there be any hope of controlling the disease. Again, statistical analysis plays a major role.
Or, the objective may simply be to know more about how the world works. So-called "pure research" has no immediate application, but seeks to find relationships among things, thereby securing knowledge that may become useful in the future.
CAREFUL STATISTICAL ANALYSIS OF DATA OFTEN RESULTS IN THE IDENTIFICATION OF DEPENDENCIES, and this is the reason why statistics is an important tool in virtually all disciplines.
3. HOW DOES THIS COURSE FIT INTO THE "GENERAL EDUCATION" PROGRAM?
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Statistics is a major way in which human beings learn about the world, and how to control it. To be familiar with a tool as fundamental and important as this is a responsibility of every educated person.
Statistics can be viewed as applied quantitative logic, usually seeking to make inferences about unknown parameters on the basis of observations and measurements of samples drawn from a target population.
The study of statistics can promote clear and careful thinking, enhance problem-solving skills, and strengthen one's ability to avoid premature conclusions. These are traits of the educated person, and are the mental qualities essential for "knowledge workers" in modern society.
4. WHAT ARE THE OBJECTIVES OF THE COURSE?
The most important objective is the development of your ability to learn this kind of material on your own, and to continue learning more about the subject after the course is over. Continuous and independent learning is an important activity of every successful person. In connection with the objective of independent learning, the instructor will expect students to study and learn certain topics in the course without formal discussion of them in class. Questions on these topics, of course, are always welcomed and encouraged.
With respect to specific objectives, they are: that students learn the terminology, theory, principles, and computational procedures related to basic descriptive and inferential statistics; and the careful cultivation of the logical processes involved in statistical inference. This will enable students to understand statistics and communicate statistical ideas using generally-accepted terminology.
Another important objective is that students become aware of the limitations of various statistical procedures. This is particularly important since most students in this course will be consumers rather than providers of statistical information and conclusions. Estimates and forecasts, for example, are generally regarded with too much faith, and relied upon to a degree not warranted in light of their inherent limitations.
5. WHAT MUST STUDENTS DO TO SUCCEED IN THIS COURSE?
Your activities in this course should include: reading and studying the relevant sections of the text; attending class and taking notes; rewriting, reviewing, and studying your notes; working the recommended exercises in the text; practicing and experimenting with various spreadsheet files supplied by the instructor; asking and answering questions in class; spending time just thinking about the procedures and their underlying logic; forming a study group with other students to review notes on terminology and concepts, and to practice problem-solving skills; and taking the quizzes.
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These activities should help you to further develop your abilities to read, listen, record, and organize important information; and to communicate, analyze, compute, and learn independently the subject matter of statistics.
In order to do well, students must recognize a basic difference between courses like statistics and courses like history, philosophy, management or organizational strategy. In the latter type, the emphasis is often on general ideas in broad contexts, with grades based on essay exams and term papers in which students have considerable latitude to choose what they are going to discuss. The cogent expression and defense of well-reasoned opinion are highly valued. Students with good verbal, logical and writing skills often excel in this type of course. Statistics, on the other hand, is a skills course, requiring precise knowledge of concepts, terminology, and computational procedures. Verbal skills are still important, but now quantitative logic and computational competence are also critical. Grades are based on knowledge of terminology and concepts, and even more on the ability to get the right answers to problems.
Regarding study strategy, it is extremely important for most students to read about statistics, to think about statistics and to do a few problems every day. The most common error is to neglect the material until shortly before a quiz. But for most students, many of the concepts in statistics are new and strange, and there will be many places where they are stopped cold: "What?" "I just don't get this!" Then there is no time left to cultivate the understanding of new concepts and to refine the computational procedures. Anyone can learn statistics, but most cannot do it overnight.
As with most courses, this course is organized with the most fundamental material coming first. In learning a new language, or how to play a musical instrument, or any new set of skills, mastery of the basics is essential to success later on. The subject matter of statistics is not like history, where, if you did not study 14th century France, it probably did not affect your learning about 17th century England. In statistics, failure to obtain a good understanding of earlier material will have a serious adverse effect on your ability to make sense out of what comes later. It is therefore essential to build a solid foundation of fundamental knowledge early in the course in order to support the more elaborate logical and computational structures involved later.
6. WHAT ARE THE PREREQUISITES FOR THE COURSE?
The primary prerequisite is a logical mind. This course is computational, but it is not a "math" course. Mathematical theorems are not derived or proven; the need to solve equations is very rare. The emphasis is on concrete applications rather than abstract theory. Some students with good math backgrounds have done poorly, while others with little or no math experience have done very well.
The best MBA stats student I ever had was a philosophy major who did not have single math course at the college level. When asked about this, the he replied: "My philosophy major gave me excellent training in logic, and that's really what this course requires."
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7. OF WHAT IMPORTANCE IS CLASS PARTICIPATION?
In this course, class participation means frequently asking relevant questions and supplying answers (right or wrong) to the instructor's and colleagues' questions as problems and examples are worked out and discussed. These behaviors are evidence of active involvement with the material and will result in better learning and an automatic positive effect on your grade. In grade border-line cases, a history of active participation will enable the instructor to award the higher grade to the deserving student.
8. WILL STUDENTS BE GIVEN ALTERNATIVE WAYS TO ACHIEVE SUCCESS, BASED ON DIFFERENT LEARNING STYLES?
Different learning styles do exist. Some prefer a deductive method (deriving specific knowledge from general principles), while others tend to prefer an inductive method (deriving the generalities from examples). The inductive learners may need to work a number of problems before seeing the patterns that are present. The deductive learners may never need to work a problem--they will know instinctively what to do. Some will not like the book, and will learn primarily from the class presentations and discussions, while others will learn mostly from the book and will find class time to be of lesser importance.
But the intended outcomes are the same for all--those in number 4 above.
9. WHAT IS THE PURPOSE OF THE ASSIGNMENTS?
Problems from the text may be suggested, for the purpose of providing practice in analyzing what must be done, and in performing the required computations. Even though computer software is available to perform calculations, students can gain insight into the logical structure of a sequence of computational steps if they go through them several times by hand (i.e. using simple calculators).
Computer assignments using instructor-supplied spreadsheet files will require students to become more familiar with spreadsheet software that they probably are or will be using in connection with their work. More importantly, the spreadsheets allow students to experiment with data in order to investigate the quantitative relationships involved. Such experimentation would be too tedious and time-consuming for manual or even calculator computation.
10.WHAT WILL THE TESTS TEST? -- MEMORY? UNDERSTANDING? ABILITY TO SYNTHESIZE? TO PRESENT EVIDENCE LOGICALLY? TO APPLY KNOWLEDGE IN A NEW CONTEXT?
The tests will test your ability to recognize and use statistical terminology correctly, and they will test your understanding of the logic and principles underlying various statistical procedures. In addition, you will have to demonstrate your ability to solve problems similar to those discussed in class, sometimes using computer spreadsheet files.
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There is a place for memorization in learning. It is not a substitute for comprehension, but it is better than getting something wrong on a quiz that you were expected to know. As with prayers among small children, memorization is often a first step, eventually followed by understanding. But if the memorization (of terminology, for example) is not done, it is less likely that the comprehension will ever occur.
11.WHY HAS THIS PARTICULAR TEXT BEEN CHOSEN?
Our text is one of the most widely adopted introductory statistics books. It has gone through several editions, and its popularity remains high. It is relatively easy to read, and its exercise material is excellent.
12.WHAT IS THE RELATIONSHIP BETWEEN KNOWLEDGE LEVEL AND GRADES?
Consider this hypothetical but realistic situation.
Percentage GradeKnowledge Course A Course B100% 100% 100%90% 90% 81%80% 80% 64%70% 70% 49%60% 60% 36%50% 50% 25%40% 40% 16%30% 30% 9%20% 20% 4%10% 10% 1%
Course A might be like philosophy, history, or management, where the grade is more-or-less proportional to knowledge level. Course B might be like statistics or other skills courses, where small deficiencies in knowledge can have disastrous effects on results. Overstudying is the best strategy for coping with this, with the dual payoffs of higher grades and, more importantly, greater knowledge.
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QUIZ HW0.667 0.333 A B C D FHW
10 20 30 40 50 60 70 80 90 95 100
QUIZ 100 70.0 73.4 76.7
80.0
83.4
86.7
90.0
93.3
96.7
98.3
100 100
95 66.7 70.0 73.4
76.7
80.0
83.3
86.7
90.0
93.3
95.0
96.7 95
90 63.4 66.7 70.0
73.4
76.7
80.0
83.3
86.7
90.0
91.7
93.3 90
85 60.0 63.4 66.7
70.0
73.3
76.7
80.0
83.3
86.7
88.3
90.0 85
80 56.7 60.0 63.4
66.7
70.0
73.3
76.7
80.0
83.3
85.0
86.7 80
75 53.4 56.7 60.0
63.3
66.7
70.0
73.3
76.7
80.0
81.7
83.3 75
70 50.0 53.4 56.7
60.0
63.3
66.7
70.0
73.3
76.7
78.3
80.0 70
65 46.7 50.0 53.3
56.7
60.0
63.3
66.7
70.0
73.3
75.0
76.7 65
60 43.4 46.7 50.0
53.3
56.7
60.0
63.3
66.7
70.0
71.7
73.3 60
55 40.0 43.3 46.7
50.0
53.3
56.7
60.0
63.3
66.7
68.3
70.0 55
50 36.7 40.0 43.3
46.7
50.0
53.3
56.7
60.0
63.3
65.0
66.7 50
45 33.3 36.7 40.0
43.3
46.7
50.0
53.3
56.7
60.0
61.7
63.3 45
40 30.0 33.3 36.7
40.0
43.3
46.7
50.0
53.3
56.7
58.3
60.0 40
30 23.3 26.7 30.0
33.3
36.7
40.0
43.3
46.7
50.0
51.6
53.3 30
20 16.7 20.0 23.3
26.7
30.0
33.3
36.7
40.0
43.3
45.0
46.6 20
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I can use Excel toperform basic computationsprepare tables create charts and graphsconduct common statistical procedurescreate dashboardshandle large data sets—“big data”
I can use Word tocreate various kinds of documents
I can compute
meansmediansvariancesstandard deviationsconfidence intervals for means and proportions
use thebinomial distribution to answer probability questions normal distribution to answer probability questionschi-square distribution to answer probability questionsF distribution to answer probability questions
conduct hypothesis tests on
the means of one group or twothe proportions of one group or twohypothetical vs. observed distributionsvariances of one group or twogroup means using ANOVA
regression analysis to examine correlation and make forecasts
I canperform financial analysiscompute the NPV of various investment opportunitiesdecide between using debt or equity to raise new fundsdetermine the optimum mix of debt and equity financingcompute cost-of-capitaldecide whether to make or buy components for our productsdetermine how much direct labor, direct materials, and overhead is going into our
productscreate cash budgetsconduct cost-volume-profit analysesprepare a master budgetprepare performance reports using standard costs and variancesemploy the scientific method to study problems that may come up
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