MATH 130 STATISTICS MOCK EXAM 1 - littrell.riomath.com

MATH 130 STATISTICS MOCK EXAM 1

Coverage: chapters 1-4 in Sullivan's Statistics.

Your actual Exam 1 will consist of thirty multiple-choice questions, worth three points each, of which you must do at least twenty-five. Practically speaking, you never want to leave any multiple-choice questions blank, because they are automatically marked wrong when you do. If you answer every one, even if you guess, you can still have a reasonable chance of guessing correctly, so it is possible you could still get points, but we're only holding you accountable for twenty-five of the multiple-choice questions. In addition, there will be five open-ended questions, of which you will need to work out in the pages of your exam paper. The five open-ended questions will be worth five points each; your exam score will be computed as a fraction of 100 points. This mock exam is a little longer than your actual exam (OK, almost twice as long). You have to understand, picking problems for mock exams is like eating potato chips... it's hard to stop. But having a nice, long mock exam is a good thing, because it gives you a lot of opportunity to practice problems which have less context than the ones in the book. Trust me, this is a real issue for a lot of people. They use the chapter section context as a crutch without even noticing that this is happening. Naturally, we want you to do well on the first exam, and on all the rest.

Remember to bring a Scantron SC882-E/N-E/E-LOVAS to the exam (there are three versions of this form, the SC882-E, the SC882-N-E, and the SC882-E-LOVAS; any of the three versions is fine); no other forms will be accepted for full credit. In addition, you will need to know your student ID number when you sit for the exam. The SC882 form has an ID number field which we will be using; if you don't know your ID number or enter it incorrectly, there will be a penalty to your score. It would also be wise to bring a legal graphing calculator. Please recall, the recommended models are anything from the TI-83/84 series. Neither computer algebra system graphing calculators (e.g., TI-89, TI-nSpire CAS), cell-phone calculators, or smart watches (e.g., iWatch) are permitted during exams. Refer to the syllabus for additional detail. When sitting for the exam, you may request a copy of the formula card from the text if you wish to use one. Finally, you will be permitted to use a single sheet of notes, no larger than 8.5" by 11". Write on one or both sides as you wish, but anything which appears on the sheet must be handwritten.

You will have a maximum of two hours to complete your exam. The proctor will time-stamp your exam; if you exceed the allocated time, your score will be reduced proportionally. For example, if you exceeded the allocated time by 12 minutes (12 minutes/120 minutes = 10%), your score would be reduced by 10%.

Finally: occasionally the algorithms behind these questions will throw a bad number, resulting in an incorrect answer on the key. If you find any inconsistencies on the key, like an apparently correct answer marked as incorrect, etc., I would greatly appreciate a heads-up. In addition, many exam bank questions are written so the answers mesh well with table use, instead of graphing calculator use. For that reason, some answers that are correct may appear to differ slightly from the answer obtained correctly on a graphing calculator. This may appear to be a roundoff error, but typically if you round the answer obtained via the calculator correctly, to the same number of places, the answers will mesh. If necessary, please email me directly regarding such items.

1. What level of measurement classifies data into mutually exclusive categories in which no order or ranking can be imposed on the data? a) ratio b) interval c) nominal d) ordinal

2. What level of measurement allows for the ranking of data, a precise difference between units of measure, and also includes a true zero? a) ordinal b) ratio c) nominal d) interval

Revision Date Spring 2018 Page 1

3. In statistics, conducting a census means:a) collecting information from all members of the populationb) making decisions based on sample resultsc) collecting a sample with replacementd) checking if a variable is qualitative or quantitative

4. Which of the following best defines the relationship between confounding, dependent, and independent variables? a) The confounding variable influences the dependent variable, but is not separated

from the independent variable. b) The confounding variable may cause the dependent variable to act independently. c) The confounding variable influences the independent variable, but has no effect on

the dependent variable. d) The influence of the confounding variable cannot be separated from the influence of

the dependent variable.

Use the following to answer questions 5-8:

In 1998 an article appeared in a British medical journal which suggested that some children may have developed Autism Spectrum Disorder (ASD) after being vaccinated against Measles, Mumps, and Rubella (MMR) with a vaccine containing small amounts of Thimerosal, a chemical compound of mercury used as a preservative. As a result of the controversy that this article created, a number of studies were conducted to explore whether or not MMR vaccines containing Thimerosal were causing ASD. One of these studies was conducted in Denmark, in 2003, and compared the rates at which ASD occurred in children who received vaccines containing Thimerosal and children vaccinated with Thimerosal-free vaccines. In Denmark, Thimerosal was used as preservative in a certain vaccine from 1970 to 1992. After 1992, it was replaced with a Thimerosal-free version. A total of 446,695 children under one year of age were vaccinated during the period of time covered by the study (1990-1996), and 1,158 of these children were later diagnosed with ASD. Of the children diagnosed with ASD, it was found that 425 were vaccinated with Thimerosal-containing vaccines, and 733 were vaccinated with Thimerosal-free vaccines. The study concluded that there was no association between Thimerosal-containing vaccines and ASD.

5. What type of study is described?a) A matched-pairs experimentb) A case-control observational studyc) A randomized block experimentd) A double-blind, completely randomized experimente) None of these.


6. What is the population being studied?a) Children worldwide d) The population of Denmarkb) The children of Denmark e) None of these.c) Children who are vaccinated in infancy

7. What is the response variable in this study?a) Whether or not the child was vaccinatedb) Whether or not the child was diagnosed with ASDc) Whether or not the Thimerosal caused ASDd) Whether or not the vaccine contains Thimerosale) None of these.

8. What is the explanatory variable in this study?a) Whether or not the child was diagnosed with ASDb) Whether or not the Thimerosal caused ASDc) Whether or not the child was vaccinatedd) Whether or not the vaccine contains Thimerosale) None of these.


A doctor wanted to determine whether increasing potassium intake would help to lower the blood pressure of patients with hypertension (high blood pressure). It is known that weight is important when it comes to controlling hypertension, so he divided the patients into three groups, based on their BMI (Body Mass Index): normal weight (BMI of 18.5 to 24.9), overweight (BMI of 25 to 29.9), and obese (BMI of 30.0 and above). Patients within each BMI group are randomly assigned to one of two subgroups. The first subgroup received no intervention; no information about the possible benefits of increased potassium intake, and nothing apart from whatever they were currently doing to manage their hypertension. The second subgroup was informed about the importance of additional potassium intake, and they were provided with a dietary supplement in the form of a nutrient-rich ready-made shake (chocolate, vanilla, or berry), which also included 50% of their recommended daily allowance of potassium, which they were to consume daily. This, in addition to whatever they were currently doing to manage their hypertension. All of the patients were provided with a blood pressure monitor and a log for recording their blood pressure twice each day; patients who logged the required number of entries over a six-month period were rewarded with a gift card from a store or restaurant of their choice. At the end of the data collection period, the blood pressure data from the groups were compared.

9. What type of experimental design is this?a) A randomized block design d) A completely randomized designb) A matched-pairs design e) None of these.c) An observational study


10. What is the response variable in this study?a) Body Mass Index (BMI) d) The potassium intakeb) The blood pressure of the patients e) None of these.c) Hypertension

11. What are the treatments?a) The dietary supplement shake containing potassiumb) The blood pressure monitors and logsc) The blood pressure of the patientsd) Body Mass Index (BMI)e) None of these.

12. What is the control group in this study?a) The patients in the first subgroup (no intervention)b) The patients in the normal weight BMI groupc) There is no control groupd) The patients in the second subgroup (dietary supplement shake with potassium)e) None of these.

13. A group of students were asked to count the number of scars on both of their hands. The number of scars on their dominant hand was compared to the number of scars on their "off" hand. Is this an observational study or a randomized experiment?a) Randomized experiment b) Observational study

14. Given the following frequency distribution, how many pieces of data were less than 28.5?

a) 17 b) 12 c) 9 d) 25 e) None of these.


23.5–28.5 1228.5–33.5 1533.5–38.5 17

Class Boundaries Frequencies13.5–18.5 418.5–23.5 9

15. Given the following table of grades and frequencies, calculate the cumulative frequency for the D class.

a) 26 b) 39 c) 24 d) 14 e) None of these.


The frequency distribution for the closing price of Apple Computer shares on 30 randomly-selected trading days from 2011 is shown below.

Class Frequency320-338.74 5338.75-357.49 8357.50-376.24 2376.25-394.99 11395-413.74 3413.75-432.49 1

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16. What is the class width of the frequency distribution for the closing price of Apple shares?a) 18.76 b) 18 c) 18.74 d) 18.70 e) None of these.


D 59.5–69.5 3F 49.5–59.5 3

Grade Class Boundaries FrequencyA 89.5–99.5 4B 79.5–89.5 7C 69.5–79.5 11

17. What is the relative frequency for the class that covers 376.25-394.99?a) 0.3953 b) 0.3667 c) 11 d) 0.8667 e) None of these.

18. In a frequency histogram, the frequency of a class is the:a) width of the corresponding barb) height multiplied by the width of the corresponding barc) area of the corresponding bard) height of the corresponding bare) None of these.

19. The procedure for obtaining the relative frequency of a class is to:a) multiply the frequency of that class by 100b) divide the frequency of that class by 100c) divide the sum of all frequencies by the frequency of that classd) divide the frequency of that class by the sum of all frequenciese) None of these.

20. Does the size of the standard deviation of a data set depend on where the center is?a) No, because the standard deviation is only measuring how the values differ from

each other.b) Yes, the higher the mean, the higher the standard deviation.c) Yes, because you have to know the mean to calculate the standard deviation.d) No, the value of the standard deviation is not affected by the value of the mean.e) None of these.

21. A 30 item math test was graded using the following procedure: a correct response was scored as +1, a blank response was scored 0, and an incorrect response was scored 1 . Using this system, the maximum possible test score was 30; the lowest score possible was 30 . The standard deviation of the test scores for the class was reported to be

2.13 . Therefore,a) the test was too hard for this class.b) a calculation error was made in determining the standard deviation.c) some students received negative scores.d) the class performed poorly on this test.e) None of these.


22. A group of 30 introductory statistics students took a 25-item test. The mean and standard deviation were computed; the standard deviation was 0. You know that:a) a calculation error must have been made in determining the standard deviation.b) everyone correctly answered the same number of items.c) the test was so hard that everyone missed all items.d) about half of the scores were above the mean.e) None of these.

23. Given that the variance for a data set is 1.20, what would be the standard deviation? a) 1.44 b) 0.60 c) 1.10 d) 1.20 e) None of these.

24. In a unimodal, symmetrical distribution as shown in the figure below:

a) The mean, the median, and the mode are the same. b) The median and the mode are the same, but the mean can be different. c) The mean, the median, and the mode are different. d) The mean is the same as the median, but the mode can be different. e) None of these.

25. A normal distribution in which approximately 68% of the data values fall within one standard deviation of the mean behaves according to a) Chebyshev's theorem. d) The Central Limit Theorem.b) Differential statistics. e) None of these.c) A symmetrical distribution.

26. If the mean of a set of data is 20.00, and 14.40 has a z-score of –1.40, then the standard deviation must be:a) 16.00 b) 8.00 c) 4.00 d) 2.00 e) None of these.


27. If a student scored 76 points on a test where the mean score was 78 and the standard deviation was 3. The student's z-score wasa) 0.22 b) –0.67 c) 26.00 d) –0.22 e) None of these.

28. Suppose the scores on an achievement test follow an approximately normal distribution with a mean of 800, a minimum value of 600, and a maximum value of 1000. Which of the following is the best estimate the standard deviation of this distribution?a) 60 b) 100 c) 400 d) 67 e) None of these.

29. Mark all which apply: Chebyshev's theorem is applicable to:a) a multimodal distributionb) a uniform distributionc) a skewed distributiond) a bell-shaped distributione) None of these.

30. Mark all which apply: the empirical rule is applicable to:a) a skewed distribution d) a multimodal distributionb) a uniform distribution e) None of these.c) a bell-shaped distribution

31. According to Chebyshev's theorem, the minimum percentage of values that fall within 4.5 standard deviations of the mean is:a) 95.06% b) 93.06% c) 92.06% d) 96.56% e) None of these.

32. According to Chebyshev's theorem, the proportion of values from a data set that is further than 1.5 standard deviations from the mean is:a) 0.17 b) 0.44 c) 0.67 d) 1.33 e) None of these.


In a certain area, in a certain local city, a statistician has gathered data on the annual incomes of all the residents. The statistician finds the mean (in thousands) to be 49.8, with a standard deviation (in thousands) of 7.3.


33. If the distribution of the income data is symmetric (bell-shaped), approximately what percent will fall between 27.9 (thousand) and 71.7 (thousand) dollars?a) At most 0.3% d) About 99.7%b) At least 88.9% e) None of these.c) At most 11.1%

34. If the distribution of the income data is not symmetric (i.e., not bell-shaped), approximately what percent will fall between 31.55 (thousand) and 68.05 (thousand) dollars?a) About 95% d) At most 84%b) About 99.7% e) None of these.c) At least 84%

35. A student received the following grades: An A in Statistics (4 credits), a A in Physics II (5 credits), a B in Sociology (3 credits), a B in a Literature seminar (2 credits), and a D in Tennis (1 credit). Assuming A = 4 grade points, B = 3 grade points, C = 2 grade points, D = 1 grade point, and F = 0 grade points, the student's grade point average is:a) 3.32 b) 3.24 c) 3.20 d) 3.47 e) None of these.

36. A test was given to 100 individuals. Half answered 80% of the questions correctly, the other half answered 90% correctly. Which of the following statements is correct, if any?a) The standard deviation is zero. d) The mean is less than the median.b) The mean is equal to the median. e) None of these.c) The mean is greater than the median.

37. A town contains four elementary schools. School A has a mean class size of 35 pupils for its four sixth-grade classrooms. School B has a mean class size of 30 pupils in its three sixth-grade classrooms. School C has 25 pupils in its two sixth-grade classrooms. School D has 20 pupils in its one sixth-grade classroom. What is the average class size for sixth-grade classrooms in this town?a) 25 b) 27.5 c) 32.5 d) 30 e) None of these.



Twice per year Forbes Magazine publishes a guide to mutual funds. The table below shows the top twenty-five stock funds as of 12/2004, ranked in terms of their five-year annual return.

Mkt Perf UP

Mkt Perf DN

Fund 5-Yr Ann Tot Ret (%)

Annual Expense Ratio

Yield (%)

A A CGM Realty Fund 29.3 1.02 0.6B A+ Hotchkis & Wiley Small Cap Value-A 28.6 1.39 0A A Bridgeway Ultra-Small Company 27.7 1.15 0B A RS Partners Fund 27.7 1.54 0D A FBR Small Cap Financial 26.1 1.57 0.5B A Wasatch Micro-Cap Fund 24.5 2.24 0F A AIM Real Estate-A 24 1.65 1.5D A Phoenix-Duff & Phelps Real Estate Secs-A 23.3 1.3 1.8D A First American Real Estate Secs-A 22.9 1.23 2.9A B Perritt MicroCap Opportunities 22.4 1.44 0D A+ Fidelity Real Estate Investment 22.3 0.86 2.3F A+ Fidelity Select--Medical Delivery 22.2 1.3 0D A American Century Real Estate-Inv 21.9 1.17 2D A AllianceBernstein Real Estate Inv-A 21.7 1.74 2.6D A+ Russell Real Estate Secs-S 21.7 1.18 3.4D A Security Capital US Real Estate 21.7 1.18 3F A Gabelli Gold Fund 21.5 1.55 1.3D A+ Cohen & Steers Realty Shares 21.3 1.07 3.2D A Delaware REIT Fund-A 21.2 1.4 2.3D A Vanguard REIT Index-Inv 21.2 0.24 4.7D A Franklin MicroCap Value-A 21.1 1.12 0.1D A+ Franklin Real Estate Secs-A 21.1 1.01 1.8D A+ PBHG Heitman REIT-PBHG 21.1 1.3 2.3D A+ Pioneer Real Estate Shares-A 21 1.68 2.7D A+ Davis Real Estate-A 20.9 1.3 1.9

The columns of the table are:Mkt Perf UP: how the fund performs in an "up" (read: increasing) market;Mkt Perf DN: how the fund performs in a "down" (read: decreasing) market;Fund: the name of the funds;5-Yr Ann Total Ret (%): the total return over the past five years, expressed as an annual percentage rate;Annual Expense Ratio: the annual expense ratio of the funds, shown as a dollar figure (per $100 invested). This is what the mutual fund companies hold back to cover their expenses.Yield (%): the annual yield of the fund (via dividends and capital gains).

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38. With respect to the mutual fund data from Forbes, what is the sample mean of the Annual Expense Ratio column?a) 0.1338 b) 0.3585 c) 0.3658 d) 1.3052 e) None of these.

39. With respect to the mutual fund data from Forbes, what is the sample variance of the Annual Expense Ratio column?a) 0.1338 b) 0.3585 c) 0.3658 d) 1.3052 e) None of these.

40. What is the interquartile range for the mutual fund annual expense ratio data?a) 1.135 b) 0.83 c) 0.41 d) 1.3 e) None of these.

41. If the average expense ratio for all funds is $1.25, with 0.36 , what is the z-score for the Gabelli Gold Fund's expense ratio of $1.55?a) 1.038 b) 1.841 c) 0.672 d) 1.922 e) None of these.


42. Given the following boxplot where m is the median value, what statement could be made about the distribution of the data?

a) The distribution is negatively skewed.

b) The distribution is approximately symmetric.

c) The distribution is positively skewed.

d) None of these.



When you buy a pair of 14K diamond stud earrings, the price increases in an approximately linear fashion with respect to the total weight of the diamonds, measured in carats. Find the regression line that gives the price (y) in terms of the total carat weight (TCW, x) of a pair of 14K diamond stud earrings.

TCW (x, in carats) 1/4 1/3 1/2 3/4 1.0 1.5Price (y, in dollars) 340 370 695 1400 2220 4615



43. The interpretation of the slope (rounded to the nearest integer) of the regression equation is:a) The slope is 3422, meaning on the average, the price of a pair of diamond stud

earrings increases by $3422 per carat.b) The slope is 3422, meaning on the average, a pair of diamond studs with a total

weight of 1 carat should cost $3422.c) The slope is 865, meaning on the average, a pair of diamond studs with a total

weight of 1 carat should cost $865.d) The slope is 865, meaning on the average, the price of a pair of diamond stud

earrings increases by $865 per carat.e) None of these.

44. The interpretation of the x-intercept (rounded to four places) of the regression equation is:a) The x-intercept is 0, meaning a pair of diamond studs with a total weight of 0 carats

would cost $0.2527, according to the regression model.b) The x-intercept is 865 , meaning a pair of diamond studs with a total weight of 0

carats would cost $865 , according to the regression model.c) The x-intercept is 3422, meaning a pair of diamond studs with a total weight of 0

carats would cost $3422, according to the regression model.d) The x-intercept is 0.2527, meaning a pair of diamond studs with a total weight of

0.2527 carats would cost $0, according to the regression model.e) None of these.

45. The interpretation of the y-intercept (rounded to the nearest integer) of the regression equation is:a) The y-intercept is 0, meaning a pair of diamond studs with a total weight of 865

carats would cost $0, according to the regression model.b) The y-intercept is 0.2527, meaning a pair of diamond studs with a total weight of

0.2527 carats would cost $0, according to the regression model.c) The y-intercept is 3422, meaning a pair of diamond studs with a total weight of 0

carats would cost 3422, according to the regression model.d) The y-intercept is 865 , meaning a pair of diamond studs with a total weight of 0

carats would cost $865 , according to the regression model.e) None of these.

46. According to the model, what would an average price be for a pair of 14K diamond stud earrings with a total weight of 1.25 carats? Round your answer to the nearest dollar.a) 3287 b) 3391 c) 3972 d) 3511 e) None of these.


47. According to the model, if a pair of 14K diamond stud earrings was being offered for $3800, what should the total carat weight be? Round your answer to the nearest hundredth of a carat.a) 1.31 b) 1.43 c) 1.36 d) 1.29 e) None of these.



Recently, the price of a gallon of gasoline on the west coast of the country has changed in a fairly predictable, seasonal pattern. In most years, the price rises to a peak in late summer, and then falls off during the winter months, and rises to a new peak the following year.

Consider the following table, which shows the monthly average gasoline price for the western United States from January, 2005 to March, 2009 . Use the x and y data in this table to answer the following questions; the x-value represents the months after January 2005 (enter into L1), and the y-value represents the price of a gallon of gasoline, in cents per gallon (enter into L2).

(Do not enter) Jan-05 Feb-05 Mar-05 Apr-05 May-05 Jun-05 Jul-05 Aug-05 Sep-05 Oct-05 Nov-05 Dec-05

x-value (use L1) 0 1 2 3 4 5 6 7 8 9 10 11

y-value (use L2) 192.3 206.6 224.5 249.4 243.7 233.2 247.1 264 297.4 285.2 249.8 225.6


x-value (use L1) 12 13 14 15 16 17 18 19 20 21 22 23

y-value (use L2) 234.5 243.2 252 281.9 321.5 314.7 313 309.9 284.9 251.9 244.2 252.5


x-value (use L1) 24 25 26 27 28 29 30 31 32 33 34 35

y-value (use L2) 254 256.9 292 318.5 336.8 322.9 306.5 285.6 283.9 299.8 326.3 322.5


x-value (use L1) 36 37 38 39 40 41 42 43 44 45 46 47

y-value (use L2) 317.6 312.9 348.1 369 388.6 437.2 436.6 402.1 375.5 332.9 243.7 182.7

(Do not enter) Jan-09 Feb-09 Mar-09

x-value (use L1) 48 49 50

y-value (use L2) 197.2 218.1 216.2


Note: these problems call for ONE regression calculation for ALL the data. Do NOT find five regression lines... just ONE. The table has been split so it will fit on the page. You can quickly fill L1 with a sequence of integers as follows: 1) clear your lists; 2) go to STAT-->EDIT; use the UP arrow key to highlight L1; 3) go to 2nd STAT (LIST) menu, select OPS; 4) select #5 seq.; 5) type in X, X, 0, 50, 1 so that the command reads seq(X, X, 0, 50, 1) and press enter. Now all you need to do is put the gas price data into L2.


48. What is the least squares line for the gasoline price data? Round all decimals to the thousandths place.a) 1.676 244.453y x d) 244.692 1.669y x b) 1.669 244.693y x e) None of these.c) 1.688 242.391y x


49. What is the practical significance of the slope of the regression equation for the gas price data?a) Between the years 2005 and 2009, on the average, every 1.669 months, the gas

price increased by $1.b) Between the years 2005 and 2009, on the average, every month, the price of gas

increased 1.669 cents.c) Between the years 2005 and 2009, on the average, every 1.669 months, the gas

price increased by 1 cent.d) Between the years 2005 and 2009, on the average, every month, the price of gas

increased $1.669.e) None of these.

50. What is the practical significance of the y-intercept of the regression model?a) The month in which the gas price, in cents per gallon, would be zero, according to

the model.b) The month in which the gas price, in cents per gallon, according to the model,

would be the same as the gas price according to the actual data.(The difference between the model price and the actual price would be zero).

c) According to the model, it is the average price, in cents per gallon, of gasoline from January 2005 to March 2009.

d) According to the model, it is the price, in cents per gallon, of gasoline in January 2005.

e) None of these.

51. According to the regression model, what should the gas price be for August 2009? Round your answer to the ten-thousands place (i.e., to the nearest tenth of a cent.)a) 339.8 b) 336.5 c) 338.1 d) 334.8 e) None of these.

52. Scatter-plot the gas price data and superimpose the regression equation over the scatter-plot. Based on the graph, the correlation coefficient, the coefficient of determination, and so forth, which of the following are true? Mark all which apply.a) Based on the combination of the regression equation graph with the scatter-plot, one

can see that gas price (y) is negatively correlated with time (x, in months).b) The linear regression model fits the gas price data well enough to be of use.c) The linear regression model accounts for more than 50% of the explained variation

in this data set.d) Using the model to predict the price of gasoline for August 2009 is an example of

interpolation.e) None of these.



After an outbreak of measles among visitors to Disneyland, a survey was taken of college students, where respondents were asked whether or not they thought parents should be required to vaccinate their children. In addition, they were asked whether or not they had children. Their responses are shown in the table below.

Should parents be required to vaccinate their children?

Do you have children of your own?

Yes No Marginal distributionYes 458 1058 1516Unsure 28 104 132No 112 229 341Marginal distribution

598 1391 1989

53. Construct a conditional distribution of respondent's attitude toward required vaccination using whether or not they have children as the explanatory variable. What proportion of people who have children responded that vaccinations should be required? Round your answer to three places.a) 0.302 b) 0.766 c) 0.230 d) 0.762 e) None of these.

54. If you construct a relative frequency marginal distribution, what proportion of respondents answered that vaccination should NOT be required? Round your answer to three places.a) 0.179 b) 0.168 c) 0.171 d) 0.165 e) None of these.

55. What conditions would need to be satisfied in order to say that a change in the variable X causes a change in the variable Y?a) When an experiment reveals that a change in X causes a change in Y.b) When possible confounding variables have been ruled out.c) When the correlation between X and Y is close to 1 .d) All of the above.e) None of these.


Open-ended questions

When you take your real exam, you will need to do FIVE of the following type of questions and answer them in the pages of your exam paper. Show all work carefully and clearly; no credit will be recorded for answers not supported by proper work.

56. The stem-and-leaf display given here shows the final examination scores of students in a statistics course. (Leaf unit = 1.0)

Stem-and-Leaf Display of Scores

a) Find the median score.

b) Find the quartiles Q1 and Q3.

c) What proportion of the students scored below 65? Round your answer to three decimal places.


4 1 1 7 95 0 3 3 6 86 0 1 2 4 4 77 2 4 4 5 5 6 8 9 98 0 2 4 5 79 0 2 3 6

2 5 73 2 4 4

Use the following to answer question 57:

Per capita annual beer consumption (in gallons) for each of the 50 states is given in the table below.

30.6 32.7 27.8 37.8 3932.4 30.4 29.3 23 30.236.4 31.3 31.3 30.2 37.427.6 28.3 35.1 41.7 19.526 34.4 33.4 33.5 31.4

33.4 30 41.5 27 29.323.2 36.8 36.6 30.6 27.935.4 37.1 44 29.6 31.333.8 31.2 43.4 28 38.229.5 26.1 24.1 37 36.4


57. Use this data to construct:

a) A raw frequency distribution with six classes;b) A relative frequency distribution with six classes;c) A cumulative raw frequency distribution with six classes;d) A cumulative relative frequency distribution with six classes;

For each, use the same six classes, with a class width of 5. Use a lower limit of 19 for the first class.


58. Find the weighted mean for three exams if the first one was worth 75 points and the student received a score of 70%, the second was worth 50 points and the student received a score of 80% and the third was worth 30 points and the student received a score of 95%? Round your answer to the nearest tenth of a percent.

59. Based on the boxplot,

complete the table.


---- ---- ---- ---- ----Minimum Q1 Median Q3 Maximum


Consider the following: the iPhone is said to hold it's resale value better than other smartphones. Data from Apple resellers and online auctions establishes the price of an iPhone 4s (16GB, no contract) changes as follows:

Monthsafter introduction

0 6 12 18

Price, $ 650 568 410 345


60. a) Use your calculator to obtain the regression equation for the iPhone price data given above. Find b) the correlation coefficient and c) coefficient of determination, and d) explain briefly what they signify.

61. If you were to graph a scatterplot of the data with the regression model superposed over it on the same graph, what would it look like, assuming you use a reasonably-sized window?


62. What are the slope and the y-intercept of the regression model, and how would you interpret them in practical terms?

63. Consider the model you found for iPhone 4s value.a) According to the model, if this iPhone 4s was selling for $450 on eBay, how long ago was it purchased?b) According to the model, what would you expect the phone to be worth 30 months after purchase?


Consider the following: researchers wanted to investigate a possible relationship between heart disease and baldness. They asked a sample of 663 males suffering from heart disease to classify their degree of baldness on a five-point scale. They also asked a control group (not suffering from heart disease) of 772 males to do the same baldness assessment. The results are summarized in the two-way table below:

Baldness None Little Some Much ExtremeHeart Disease 251 165 195 50 2Control 331 221 185 34 1

64. Calculate the proportion of heart disease patients who report some or more (i.e., some, much, or extreme) baldness. Also calculate the proportion of control group patients who report some or more baldness.

65. What conclusion can you draw regarding a possible relationship between baldness and heart disease?

66. Can the authors of the study say that heart disease is a cause of baldness, or vice-versa? Explain briefly.


Use the following to answer question 67:

After an outbreak of measles among visitors to Disneyland, a survey was taken of college students, where respondents were asked whether or not they thought parents should be required to vaccinate their children. In addition, they were asked whether or not they had children. Their responses are shown in the table below.



Yes No Marginal distributionYes 458 1058 1516Unsure 28 104 132No 112 229 341Marginal distribution

598 1391 1989

67. Is having children associated with one's attitude toward whether vaccination should be required, or not?


Sample Bonus Questions

On each exam, I like to include some optional questions that allow people with a deeper understanding of the subject material to demonstrate this. I call these questions "bonus questions," and I handle them in the following way: if you attempt any bonus question and get it wrong, I won't take off any points. If you get it right-- it has to be 100% correct-- you can earn 10 bonus points per question, and you can submit up to two bonus problems per exam. Anything you submit in response to a bonus question needs to be "camera ready," meaning it needs to be clear, relatively free of confusion, and it needs to read like one of the solutions you've seen in the text-based examples and/or your solution manual. Since we don't take points off when you make a mistake on one of these questions, we don't award partial credit, either. Thus, if you're unwilling or unable to write things up in this clear fashion, feel free to skip these questions.

Too, if you'd like some additional questions to study, check out the problems labeled "Putting it together," which can be found near the end of most exercise sets in each section of your text.

68.

[Sample Bonus] Consider the infographic above. What (if anything) is wrong with this?


69. [Sample Bonus] Construct a data set of 10 hypothetical exam scores (use integers between 0 and 100) so that the inter-quartile range equals zero and the mean is greater than the median. Calculate the IQR, median, and mean to show that your answer satisfies the requirements as stated.

70. [Sample Bonus] A certain basketball team played 81 games last year. The team averaged 90 points per game with a standard deviation of 10 points per game. I am interested in finding two values X and Y representing points scored, such that in at least 45 of the games played by the team, they scored between X and Y points. Find X and Y.


Answer Key

1. c2. b3. a4. a5. b6. c7. b8. d9. a

10. b11. a12. a13. b14. d15. e16. e17. b18. d19. d20. a21. b22. b23. c24. a25. e26. c27. b28. d29. a, b, c, d30. c31. a32. b33. d34. c35. d36. b37. d38. d39. a40. c41. e42. b43. a44. d


45. d46. e47. c48. b49. b50. d51. b52. e53. b54. c55. d56. a) 65.5

b) Q1 = 50, Q3 = 79

c) 0.557. The answer is best organized into a single table, much like what you see in our text.

58. 75 0.7 50 0.8 30 0.95

0.7806...75 50 30

or 78.1%

59.

60. a) The calculator returns 17.883 654.2y x .

b) The correlation coefficient is 0.987 (rounded to three places).c) The coefficient of determination is 0.975 (rounded to three places).d) The correlation coefficient is a measure of how well the data fits this linear model. In this case, as you can see from the scatter plot, we have a strong, negative linear correlation ( 0.987 ). The coefficient of determination is a measure of what proportion of the change in the price (y) is accounted for by the model (i.e., the regression model). In this case, the model accounts for 97.5% of the change in the value over time.


12 0.2429-33.9 21 0.42 33 0.6634-38.9 12 0.24 45 0.9039-43.9 4 0.08 49 0.9844-48.9 1 0.02 50 1.00

ClassRaw

FrequencyRelative

Frequency

CumulativeRaw

Frequency

Cumulative Relative Frequency

Minimum Q1 Median Q3 Maximum4 13.5 21.5 26 36

19-23.9 3 0.06 3 0.0624-28.9 9 0.18

61. The calculator produces the following graph, using a window of [ 2 , 20] by [0, 700].

A prettified version of the graph appears below.

62. The slope is 17.883 dollars

17.8831 month

, meaning that according to the model, the value

of this particular model of iPhone 4s depreciated/decreased by $17.88/month, on the average.

The y-intercept is $654.2, or more specifically, 0,654.2 , meaning that according to

the model, the purchase cost (cost at 0t ) of this particular model of iPhone 4s would be $654.20. As an aside, why would this differ from the actual purchase price? It's from a regression model, and often the model fails to contain particular data values. In fact, if you look at the prettified version of the graph (or, if you look carefully at the graph in the calculator, zooming in as needed), how many of the actual data values are contained by the model, or (to put it differently) lie on the regression line? None are contained. So the fact that the y-intercept according to the data varies from the y-intercept according to the model shouldn't be surprising. (It would be surprising if the model did contain one of the actual data values.)


63. Part a) is an example of "given y, find x." Our expectation is that you read this question

and think "$450 is a y-value. They are asking me to solve 450 17.883 654.2x for x," or something to that effect. You can do this with the calculator, as you may have seen in the videos we have linked for you on the Course Web Page. You should be able to get your calculator to spit out the following graph:

From this we conclude the solution is 11.418x months, which is a bit less than a year after the phone was purchased.

Regarding part b), this is an example of "given x, find y." We're expecting you to read this and realize "30 months is an x-value. They are asking me to evaluate

17.883 654.2y x at 30x ," or something to that effect. You can also do this with the calculator, but your window (assuming you are using the same one from above) needs to be enlarged before the calculator will do this for you. In other words, if the calculator does not see 30x in the window, this won't work. Using the method shown in the video, you ought to be able to get your calculator to spit out the following graph:

From which you can see the model predicts the value of the phone will be $117.70.64.

For those with heart disease, the total proportion with some or more baldness is 0.294 0.075 0.003 0.372 ; For the control group, the proportion with some or more baldness, the equivalent figure is 0.240 0.044 0.001 0.285 .


Some Prop. Much Prop. Extreme Prop.Heart Disease

251 0.379 165 0.249 195 0.294 50 0.075 2 0.003

Control 331 0.429 221 0.286 185 0.240 34 0.044 1 0.001

Baldness None Prop. Little Prop.

65. The proportion of men with significant baldness (some + much + extreme) is 0.372, which is significantly higher than the equivalent figure from the control group (0.285). This suggests there may be some association (or correlation) between baldness and heart disease. But remember, correlation is not the same as causation.

66. No, aside from the fact that it borders on absurdity to suggest that baldness could somehow cause heart disease, or vice-versa, this was an observational study, and observational studies can never be used to establish a causal relationship. If the correlation is well-established, in all likelihood there is a lurking variable (or variables) which would account for the correlation.

67. The conditional distribution (using whether or not respondents have children as the explanatory variable) is shown below.

In this case, the proportion of respondents in each row-- Yes, Unsure, or No-- is very close. For example, roughly 76% of individuals responded Yes, regardless of whether they have children or not. So it would appear that there is no association. In other words, responses appear to be independent of whether or not the respondent has children or not.

Later (chapter 12) we'll revisit this table and test for association more formally.


Yes No Marginal distribution

Yes 0.766 0.761 1516Unsure 0.047 0.075 132No 0.187 0.165 341Marginal distribution

598 1391 1989



68. The oil barrels are supposed to be comparable to the bars of a bar chart, a.k.a. histogram, but there is no correlation between the height of the barrels and the numbers they represent. $195,973 is nearly three times larger than $67,966, but the larger barrel is only about twice as tall as the smaller barrel. In terms of area, the ratio is closer to being correct; the area occupied by the larger barrel is approximately three times the area occupied by the smaller barrel, which makes it acceptable from that perspective. In my experience, however, it is unusual to find creators of infographics who are careful to make sure their graphic represents the data properly in any respect (whether it be on the basis of one-dimensional height or two-dimensional area). It is easy to find examples of bad infographics.

Violations of the "area priciple," as it is commonly known are far more common in infographics than many realize. The right-hand side of the image below shows a violation of this principle; the left-hand side shows the proper scale with the bar chart. Basically the right-hand graphic is wrong, because the area of the larger coin (representing roughly $2 million) is about 100 times the area of the smaller coin (representing $200,000), whereas $2 million is only TEN times larger than $200,000. So in effect, the area of the large coin exaggerates the ratio of the two values by a factor of ten.

There is a way to quantify the extent to which an infographic distorts the truth, which we call the "lie factor." To compute this, you take the following ratio:

size of the effect according to graphlie factor =

size of effect according to dataIn this case, the lie factor of the right-hand graph (measuring the radii of the circles using a ruler, or using the scale on the vertical axis) is:

41000.04 10

2000000 200000 10

as explained above.


69. Many answers are possible. One set that works would be: 40, 40, 40, 40, 40, 40, 40, 40,90,90 . The IQR is 0; the median is 40, and the mean is 50.

70. Use Chebyshev's theorem. From 2

1 451

81k , you should be able to show clearly that

3

2k ; from this it follows the team will score between 90 15 points, or 75 and 105

points for at least 45 of the 81 games. If you want to get credit for a question like this, you need to show, in detail, how this follows. A "camera-ready" answer would look something like this:Chebyshev's theorem says that the proportion of the distribution that lies within k

standard deviations of the mean is at least 2

11

k . So

2 2 2

1 45 45 1 36 11 1

81 81 81k k k , and therefore 2 81

36k , so that

81 9 3

36 6 2k .

Since 90 and 10 , 390 10 90 15

2k , so the team scored between

75 and 105 points in at least 45 of the 81 games. Or something to that effect. The basic idea with this type of problem is that you want to avoid the suggestion of even the merest hint of confusion on your part, so you want the answer to be clear and very well-supported.


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MATH 130 STATISTICS MOCK EXAM 1 - littrell.riomath.com