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Economic Statistics
WO R K T E X T
Pangasinan State UniversityLINGAYEN CAMPUS
Lingayen, PangasinanPAN
GA
SIN
AN STATEUNIVE
RSITYPA
NG
AS
INAN STATE UNIV
ER
SITY
1979
Jameson N. Estrada
Pangasinan State University
PREFACE
Economic Statistics with the course code Econ 122 uses the tools of statistics asapplied to research and economics. It is designed to present various statistical conceptsor methods that would describe and interpret data to come up with a decision throughforecasting or predictions and give empirical content to economic relations for use astandard measure of business and economic performance. To ensure the course objectiveswould be achieved, a need for a teaching resource material is necessary. Thus, this worktexthas been prepared.
The worktext is intended for use by students of AB Economics program taking up thesubject Econ 122 with the objective of providing them with a comprehensive understandingcomprehensive framework for consistent reasoning and analysis of economic data. Likewise,it has been designed as an instrument for learning development and assessment, providingstudents with a practical approach to applying the knowledge learned in the lectures. Eachworktext covers exercises that is built upon the lessons of all the chapters with the followingcourse outcomes:
1. Demonstrate an understanding of the nature, scope and significance of statistics asapplied to economic statistics.
2. Understand how to organize and graph qualitative economic data.3. Analyze location, variability and association of data using statistical measures like
mean, median, mode, range, standard deviation, and variance.4. Use probability to measure the degree of uncertainty of events occurring in economic
and business problems.5. Apply a working understanding of probability distributions (normal and binomial).6. Analyze and use sampling distributions to provide a major simplification on the route
to statistical inference.7. Conduct hypothesis testing to determine whether a statement about the value of a
population parameter should be rejected or should not be rejected.8. Analyze the techniques for modeling and analyzing the relationship between a dependent
variable and one or more independent variables using regression analysis.9. Analyze the strength and direction of statistical relationship between two random
variables or two sets of data using correlation analysis.10. Analyze the significant difference between or among variables using ANOVA.11. Utilize non-parametric inferential statistical methods which are mathematical
procedures for statistical hypothesis testing.
Bear in mind that it takes sustained effort – and some dedicated patience – to studyand learn the subject. But, it is assured that the effort is well worth it. It is hoped thismodest work helps you. So, the best of luck as you begin your journey in answering theworktext exercises!
TABLE OF CONTENTS
1 Introduction to Economic Statistics
4 Organizing and Graphing Data
9 Statistical Measures of Data
14 Probability
Normal Probability Distribution
18 Sampling Distribution
21 Test of Hypotheses
24 Regression
28 Correlation
31 Non-Parametric Method of Statistics
CONTENTPAGE
1
WORKTEXT 1 : Introduction to Economic Statistics Econ 122 – Economic Statistics
www.jamesonestrada.com
EXERCISE 1 Identification. Identify the following. Write the answer in the blank after the question.
1. A group of methods used to collect, analyze, present, and interpret data and to make decisions. ____________________
2. It consists of methods for organizing, displaying, and describing data by using tables, graphs, and summary measures. ____________________
3. The selection of a few elements from the population. ____________________
4. A mathematical notation that is used to denote the sum
of values. ____________________
5. The facts and figures collected, analyzed, and summarized for presentation and interpretation. ____________________
6. This consists of methods that use sample results to help make decisions or predictions about a population. ____________________
7. A qualitative variable that incorporates an ordered position, or ranking. ____________________
8. A qualitative variable that characterizes or describes an element of a population. ___________________
9. A characteristic under study that assumes different values for different elements. ____________________
10. A variable that can assume any numerical value over a certain interval or intervals. ____________________
11. A collection of observations on one or more variables. ____________________
12. It consists of all elements—individuals, items, or objects—whose characteristics are being studied. ____________________
13. A portion of the population selected for study is referred
to as a sample. ____________________
14. These are data that can be measured numerically. ____________________
15. A variable whose values are countable and can assume only certain values with no intermediate values. ____________________
EXERCISE 2 A. Classification. Indicate whether each of the following applies to descriptive statistics or inferential statistics. Write D for descriptive and I for inferential. .
16. Average weekly profits earned by market vendors in a public market __________
17. Linear correlation between a country’s gross domestic product (GDP) and its level of technology __________
18. Probability that the better team, Team A, will win the series if it is a one-game series __________
19. Use of 2.5% significance level to predict that the production process should be stopped to make necessary adjustments __________
20. Cumulative relative frequency distribution for the
monthly debt of 100 teachers __________
21. Regression analysis between the relationship between food expenditure and income of a household __________
22. Variance of the number of rooms for the nine hotels surveyed __________
23. Null and alternative hypotheses to test whether the mean yields for the four rice varieties are the same __________
24. Percentage of the LED TVs sold last month which includes the two new models __________
25. Test of hypothesis at the 10% significance level whether the current distribution of exercise frequency differs from that of May 2014 __________
26. Median sales price of new houses developed by Amaia Land. __________
27. The test at the 1% significance level whether the mean relief time for Brand A is less than that for Brand B. __________
28. The predictive regression equation of the prices of tea on the demand for coffee __________
Republic of the Philippines Pangasinan State University
Lingayen Campus
WORKTEXT 1 : INTRODUCTION TO ECONOMIC STATISTICS Econ 122 – Economic Statistics
NAME: _______________________________________ SCORE: ___________________________________ YEAR AND COURSE: ___________________________ DATE: ____________________________________
2
WORKTEXT 1 : Introduction to Economic Statistics Econ 122 – Economic Statistics
www.jamesonestrada.com
29. A linear correlation between time spent by a student on the social networking site Facebook and grade point average __________
30. The range of the number of hotdogs consumed by 10
participants in a hotdog-eating contest __________
31. The test at the 1% significance level by p-value approach to conclude that the company’s claim is true __________
32. The average inflation rates of a country from 2008 to 2013 __________
33. The mode of the numbers of hours spent partying by 60 randomly selected college students during the past week __________
34. The standard deviation of customers entering a grocery store during a 1-hour interval __________
35. Correlation coefficient between calories and popular protein foods (fresh red meats, poultry, and fish) __________
36. The strong empirical relationship between the size of a country’s economy and the volume of its exports and imports. __________
B. Classification. Identify whether each of the following constitutes a population or a sample. Write P for population and S for sample.
37. Gross sales for 2013 of selected four fast-food chains __________
38. The number of all unemployed individuals in a city conducted by NSO __________
39. Credit card debts of sixty families selected from a city.
40. Number of points scored by all Azkal players in the 2013
soccer games __________
41. Number of parole violations by all 1,000 parolees in a city jail __________.
42. Amount spent on prescription drugs by 320 senior
citizens in a large city __________
43. Number of personal fouls committed by all PBA players during the 2012–2013 season __________
44. Yield of potatoes per hectare for 10 farmlands in La
Trinidad __________
45. Weekly salaries of all employees of a company __________
46. Goats owned by 100 farmers in a municipality _________
47. Number of computers sold during the past week at all
computer stores in Metro Manila __________
48. A group of 35 patients randomly selected to test a new drug __________
49. Total output produced on a machine for each year from
2000 to 2013 __________
50. Yearly expenditures on clothes for 50 households in a city __________
51. Number of houses sold by each of the 10 real estate
brokers a real estate agency during 2012 __________
52. Salaries of sales managers of all companies in Metro Manila __________
53. Five hundred households selected from a city on a
marketing survey __________
54. Annual incomes of all 33 employees of a restaurant __________
55. The percentage of all voters in a province who will vote
for a particular candidate in an election __________ C. Classification. Identify which type of variable and relationship is represented by the following. Write D for dependent variable, and I for independent variable.
56. Price __________ Quantity demanded __________
57. GDP __________
Imports __________
58. Weekly income __________ Weekly food expenditure __________
59. Total cost __________ Production volume __________
60. Study time __________ Examination score __________
61. Person’s age __________ Person’s height __________
62. Automobile’s horsepower __________ Gasoline mileage __________
63. No. of rice yields __________ Amount of fertilizer __________
64. No. of units demanded __________ Price of a substitute good __________
65. The level of enrollment __________ Amount of tuition fee__________
66. Total gross sales __________ Amount of money spent on advertising __________
67. Number of major natural calamities __________ Annual profits of an insurance company __________
3
WORKTEXT 1 : Introduction to Economic Statistics Econ 122 – Economic Statistics
www.jamesonestrada.com
68. Calorie Count __________ Amount of carbohydrates __________
69. No. of retail spaces rented __________ Rental fee __________
70. Coffee sales __________ Temperature __________
D. Classification. Identify which level of measurement is represented by the following data. Write N for nominal, O for ordinal, I for interval and R for ratio.
71. Years covered by Spanish rule and settlement in the Philippine history from 1565 – 1898. __________
72. Monthly income of club members in a yoga class: P15,000–P30,000 __________
73. Course grades in any course: 1.0, 1.25, 1.5. 1.75. 2.0,
2.25, 2.5, 2.75, 3.0 __________
74. Student’s sex: male, female __________
75. The number of accidents that occur on a given highway during 1-week period __________
76. Average monthly temperature in degrees Celsius in Metro Manila throughout the year __________
77. Average daily rainfall in inches in Dagupan City
throughout the month __________
78. Education level of survey respondents __________
79. Marital status of survey respondents __________
80. Age of the respondents in the survey __________
81. Gender of the respondents in the survey __________
82. The year in which the respondent was born __________
83. The voting intentions of the respondents in the survey classified as Pro, Anti, or Undecided __________
84. The race of the respondents in the survey classified as
European, African, American, Asian, or Other __________
85. Performance rating of employees classified as Above
Expectations, Average Expectations, or Below Expectations __________
86. The uniform number of each member on a sports team
__________
87. A list of the graduating high school seniors by class rank __________
88. Final exam scores for an economics class on a scale of
0 to 100 __________
89. The municipality in which the respondents in a survey reside __________
90. A poll of registered voters as to which candidate they
support. __________ E. Classification. For each of the following, determine whether the variable or data being measured is qualitative or quantitative. Write QL for qualitative and QN for quantitative.
91. The hair color of adults auditioning for a reality show __________
92. The number of stop signs in towns of fewer than 5,000
people __________
93. Whether or not a laser printer is defective __________
94. Number of questions answered correctly on a pre-test __________
95. Length of time required to answer a telephone call at a
certain real estate office __________
96. The average number of television sets sold at an appliance store during a given week __________
97. Status of an undergraduate college student __________
98. Colors of cars __________
99. Marital status of respondents __________
100. Time to commute from home to work __________
101. Prices of personal consumer goods in department store
__________
102. Women’s favorite TV programs __________
103. Salaries of football players __________
104. Number of pets owned by families __________
105. Favorite breed of dog for each of 20 persons __________
106. Number of typographical errors in newspapers
__________
107. Monthly TV cable bills__________
108. Sales of imported garlics from China__________
109. Amount of profit earned by rice farmers. __________
110. Number of units demanded for chairs __________
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WORKTEXT 1 : Introduction to Economic Statistics Econ 122 – Economic Statistics
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F. Classification. For each of the following, determine whether the variable or data being measured is discrete or continuous. Write D for discrete and C for continuous.
111. Number of friends in Facebook __________
112. Family size (number of siblings) __________
113. Preference between laptop and tablet __________
114. Number of correct answers on an economics quiz __________
115. Annual budget of each government department
__________
116. Number of accidents that occur on a given highway during a 1-week period __________
117. Costs incurred by a paper manufacturing firm. __________
118. Grade point average, GPA, of any student __________
119. Market value of Philippine GDP in 2013 __________
120. Number of electric fans within a household __________
121. Length of time required for a wound to heal when a new
medicine is being used __________
122. Gross sales of 12 ice cream parlors in April 2014 __________
123. Restaurant bill of a family for each month of 2013 __________
124. Number of typhoons each year in the Philippines from
1987 to 2013 __________
125. Number of supermarkets in Metro Manila __________
126. Average prices of condominium units in Makati City.
127. Salaries of 60 employees __________
128. Number of cars sold each year by Ford from 2006 to 2013 __________
129. Number of employees employed by a company each year from 2001 to 2014 __________
130. Lottery revenues earned by PCSO __________
EXERCISE 3 Problem Analysis. Analyze and answer what is required in the following problems. A. The number of shoe pairs owned by six women is 8, 14, 3, 7, 10, and 5, respectively. Let 𝑥 denote the number of shoe pairs owned by a woman. Find
131. ∑𝑋
132. ∑𝑋2
133. (∑𝑋)2 B. The number of restaurants in each of six small towns is 4, 12, 9, 10, 7 and 5, respectively. Let 𝑦 denote the number of restaurants in a small town. Find
134. ∑𝑦
135. ∑𝑦2
136. (∑𝑦)2 C. For the following scores, find the value of each expression: 16.52, 4.35, 12.54, 7.96, 11.25, and 8.34.
137. ∑𝑋
138. ∑𝑋2
139. (∑𝑋)2
140. ∑𝑋 − 1
141. ∑(𝑋 − 1)
142. ∑(𝑋 − 1)2 D. Two scores, 𝑋 and 𝑌, are recorded for each of 𝑛 = 5 subjects. For these scores, find the value of each expression.
143. ∑𝑋
144. ∑𝑌
145. ∑𝑋𝑌 E. The accompanying table lists six pairs of 𝑥 and 𝑦 values.
𝑥 6 12 8 5 14 21
𝑦 4 15 6 10 9 20 Compute the value of each of the following.
146. ∑𝑦
147. ∑𝑥2
148. ∑𝑥𝑦
149. ∑𝑥2𝑦
150. ∑𝑦2
Subject
𝑿
𝒀
A 4 5 B 0 8 C 2 4 D 3 2 E 2 4
1
WORKTEXT 2 : Organizing and Graphing Data Econ 122 – Economic Statistics
www.jamesonestrada.com
EXERCISE 1 True or False. Determine whether each of the following statements is true or false. If false, underline the word or phrase to make the statement correct. Write your answer on the blank provided after the question.
1. Before they are processed and ranked, raw data are recorded in the sequence in which they are collected. _____________
2. A frequency distribution for quantitative data lists all
categories and the number of elements that belong to each of the categories. _____________
3. The relative frequency of a category is obtained by
multiplying the relative frequency of that category by 100. _____________
4. A pie graph is made of bars whose heights represent the
frequencies of respective categories is called a bar graph. _____________
5. The class boundary is determined by the midpoint of the
lower limit of one class and the upper limit of the next class. _____________
6. The class width is also called the class size.
_____________
7. Each class in a cumulative frequency distribution table gives the total number of values that fall below a certain value. _____________
8. If the observations in a data set assume only a few
distinct (integer) values, it may be appropriate to prepare a frequency distribution table using single-valued classes. _____________
9. The cumulative relative frequencies are obtained by
dividing the cumulative frequencies by the total number of observations in the data set. _____________
10. A histogram is a graph in which classes are marked on
the vertical axis and the frequencies are marked on the horizontal axis. _____________
11. When plotted on a diagram, the cumulative frequencies
give a curve that is called a polygon. _____________
12. A symmetric histogram is identical on both sides of its central point. _____________
EXERCISE 2 Problem Analysis. Analyze and answer what is required in the following problems. A. The following data give the results of a sample marketing survey. The letters A, B, and C represent the three categories.
13. Prepare a frequency distribution table.
14. Calculate the relative frequencies and percentages for
all categories.
15. What percentage of the elements in this sample belong to category B?
16. What percentage of the elements in this sample belong
to category A or C? B. The data on the type of unemployment of 50 unemployed people are represented below. These are represented by these categories: FU (frictional unemployment), SU (seasonal unemployment), CU (cyclical unemployment), TU (technological unemployment), RU (residual unemployment).
FU CU TU FU CU FU CU FU TU CU SU FU TU SU FU FU TU SU FU SU CU FU FU CU SU RU FU FU SU SU FU FU RU FU RU RU FU RU SU RU TU CU CU TU CU FU FU CU FU FU
17. Prepare a frequency distribution table.
18. Calculate the relative frequencies and percentages for
all categories.
19. What percentage of the elements in this sample belong to category CU?
20. What percentage of the elements in this sample belong
to category FU?
21. Draw a bar graph for the frequency distribution.
22. Draw a pie graph for the frequency distribution.
A B A C B B A C B B A B B C C C C C A C A C B C C B C B C B C C B A A C
Republic of the Philippines Pangasinan State University
Lingayen Campus
WORKTEXT 2 : ORGANIZING AND GRAPHING DATA Econ 122 – Economic Statistics
NAME: _______________________________________ SCORE: ___________________________________ YEAR AND COURSE: ___________________________ DATE: ____________________________________
1
WORKTEXT 3 : Statistical Measures of Data Econ 122 – Economic Statistics
www.jamesonestrada.com
EXERCISE 1 True or False. Determine whether each of the following statements is true or false. If false, underline the word or phrase to make the statement correct. Write your answer on the blank provided after the question.
1. A measure of central tendency gives the center of a histogram or a frequency distribution curve. __________
2. The mean for ungrouped data is obtained by dividing the sum of all values by the number of values in the data set. __________
3. The median is the value of the middle term in a data set that has been ranked in increasing order. __________
4. Mode represents the most common value in a data set. __________
5. Probably the median is the most used measure of central tendency. __________
6. The mode is a better measure when a data set includes outliers. __________
7. For a histogram and a frequency distribution curve skewed to the left, the value of the mean is the largest that of the mode is the smallest, and the value of the median lies between these two. __________
8. The range is obtained by taking the difference between the largest and the smallest values in a data set. __________
9. The value of the standard deviation tells how closely the values of a data set are clustered around the variance. __________
10. The standard deviation is obtained by taking the positive square root of the mean. __________
11. To calculate the mean for grouped data, first find the midpoint of each class and then multiply the midpoints by the frequencies of the corresponding classes. __________
12. Empirical rule gives a lower bound for the area under a curve between two points that are on opposite sides of the mean and at the same distance from the mean. __________
EXERCISE 2 Problem Analysis. Analyze and answer what is required in the following problems. A. The following are the personal savings (in thousands) of all nine employees of a small company.
120 245 45 87 125 226 132 15 65
13. Find the mean savings of these employees. B. The table reveals the number of PCs (in million units) shipped by each manufacturer in 2013.
PC Manufacturer 2013 Shipments (million units)
Lenovo 53.2 HP 51.2 Dell 36.7 Acer Group 25.6 Asus 25.1 Others 128.9
14. Find the mean shipments of PC manufacturers.
C. The following data give the prices (in thousands of pesos) of seven house and lot selected from all houses sold last month in a subdivision.
856 765 790 812 834 823 776
15. Find the median. D. Suppose the following data give the 2013 gross domestic product (GDP) in billions of dollars for 32 countries.
166 450 776 604 1134 288 236 678 323 621 1246 813 540 147 632 1028 1546 884 423 509 350 402 537 757 678 122 213 334 779 873 509 911
16. Calculate the mean and median for these data. Are
these values of the mean and the median sample statistics or population parameters? Explain.
17. Do these data have a mode? Explain.
Republic of the Philippines Pangasinan State University
Lingayen Campus
WORKTEXT 3 : STATISTICAL MEASURES OF DATA Econ 122 – Economic Statistics
NAME: _______________________________________ SCORE: ___________________________________ YEAR AND COURSE: ___________________________ DATE: ____________________________________
2
WORKTEXT 3 : Statistical Measures of Data Econ 122 – Economic Statistics
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E. The data below reveals the top 10 largest exporters of rice in the world.
Country Exports (Thousand Metric Tons)
Thailand 8,500 Vietnam 6,500 Pakistan 3,800 India 2,200 Cambodia 850 Uruguay 700 China 600 Egypt 600 Argentina 500 Brazil 400
18. Calculate the mean.
19. Calculate the median.
20. Calculate the mode.
F. The table below reveals the Philippine Gross Domestic Product (GRDP) measured at regional levels in 2013.
Region GRDP (in billion PHP)
Metro Manila 3,479 Cordillera 210 Ilocos 294 Cagayan Valley 167 Central Luzon 883 CALABARZON 1,645 MIMAROPA 176 Bicol 207 Western Visayas 395 Central Visayas 602 Eastern Visayas 243 Zamboanga Peninsula 201 Northern Mindanao 467 Davao Region 408 SOCCSKSARGEN 262
21. Calculate the mean.
22. Calculate the median.
23. Calculate the mode.
G. The following data represents the prices of seven economics textbooks randomly selected from a bookstore.
225.50 435.75 352.25 387.25 496.5 288.75 504.25
24. Find the median for these data. H. Last year’s incomes of six randomly selected families were P450,150, P255,650, P180,785, P385,490, and 273,740.
25. Find the mode.
I. The following data give the tax revenues (in billions of pesos) of the six cities in Metro Manila for the year 2013. The data represent the following cities, respectively: Quezon (245.5), Manila (176.4), Makati, Taguig (114.5), Pasig (133.8) and Mandaluyong (184.8).
26. Find the mean and median for these data. J. Suppose the following table gives the frequency distribution of the declared assets (in million pesos) by 36 candidates during a senatorial election.
Declared Assets (in millions of pesos)
Number of Candidates
0 to 3 4 4 to 6 12 7 to 9 9 10 to 12 8 13 to 15 3
27. Find the mean for these grouped data.
K. The following table gives the frequency distribution of the number of hours spent per week playing online games by selected 45 first year students at a university.
Hours per week Number of Students
0 to 4 6 5 to 9 11 10 to 14 16 15 to 19 10 20 to 24 2
28. Find the mean for these grouped data.
L. The following gives the sample of six purchases of fertilizers of a certain farm over the past five months.
Purchase Cost per kilo
Number of kilos
1 42 850 2 11 210 3 35 690 4 62 1,200 5 51 1,070 6 26 450
29. Calculate the weighted mean.
EXERCISE 2 Problem Analysis. Analyze and answer what is required in the following problems. A. The following data give the numbers of pieces of email spam received by 12 call center agents during the past month.
6 24 2 12 16 30 8 9 17 15 12 3
30. Find the range.
3
WORKTEXT 3 : Statistical Measures of Data Econ 122 – Economic Statistics
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B. The following data represents the hourly wage rates (in pesos) of selected six employees of a particular company.
60 120 220 180 110 95 155 120
31. Calculate the first quartile.
32. Calculate the third quartile.
33. Calculate the 20th, 25th percentiles.
34. Calculate the 65th and 75th percentiles. C. Solve the following data.
35. Calculate the variance, standard deviation, and the range for the following sample data set: 27, 18, 23, 11, 8, 19, 25, and 31.
36. Calculate the variance and standard deviation for the following population data set: 84, 82, 90, 77, 75, 77, 82, 86, 82.
37. Calculate the variance and standard deviation and the range for the following sample data set: 31.24, 24.26, 44.97, 25.66, 29.45, 21.45, 10.44 and 36.33.
D. The following table gives the 2013 market values (rounded to billions dollars) of seven IT companies.
Company Market Value (billions of dollars)
Apple 342 Google 251 Microsoft 278 Samsung 312 Intel 78 LG 156 HTC 55
38. Calculate the variance for these data.
39. Calculate the standard deviation for these data.
E. The table reveals the number of smartphone units shipped by each smartphone brand in 2013.
40. Calculate the variance for these data.
41. Calculate the standard deviation for these data.
F. The following table gives the frequency distribution of the number of selfie pictures posted on Facebook by 50 instructors at a university.
Hours per Week
Number of Students
1 - 10 4 11 - 20 11 21 – 30 15 31 - 50 12 51 - 60 8
42. Calculate the variance for these data.
43. Calculate the variance for these data.
G. The following shows the frequency distribution of the prices of milk tea.
Prices Quantity Demanded
1 – 20 110 21 – 40 85 41 – 50 67 51 – 60 45 61 – 70 32 71 – 80 24
81 – 100 8
44. Calculate the variance.
45. Calculate the standard deviation. H. The mean time taken by all participants to run a road race was found to be 220 minutes with a standard deviation of 20 minutes. Using Chebyshev’s theorem, find the percentage of runners who ran this road race in
46. 180 to 260 minutes
47. 160 to 280 minutes
48. 170 to 270 minutes I. Suppose the average credit card debt currently by JNE employees is P9500 with a standard deviation of P2600.
49. Using Chebyshev’s theorem, find at least what percentage of current credit card debts for all households are between P4,300 and P14,700 and P3000 and P16,000
50. Using Chebyshev’s theorem, find the interval that
contains credit card debts of at least 89% of all employees
Smartphone Brand 2013 Sales (in million units)
Samsung 311.4 Apple 153.4 Huawei 52 LG 47.6 Lenovo 46.2 ZTE 40.1 Sony 38.4 Coolpad 35.3 Nokia 30.5 HTC 26.6
EXERCISE 1
True or False. Determine whether each of the following statements is true or false. If false, underline the word or phrase to make the statement correct. Write your answer on the blank provided after the question.
1. The normal probability distribution is applied to a discreterandom variable. __________
2. The form or shape of the normal distribution is illustratedby the cone-shaped normal curve. __________
3. The highest point on the normal curve is at the mean,which is also the median and mode of the distribution.__________
4. The total area under the curve for the normal distributionis 1. __________
5. The probability that 𝑥 assumes a value in any interval liesin the range 0 to 1. __________
6. The z value for 𝜇 for a normal distribution curve is alwayspositive. __________
7. The 𝜇 and the 𝜎2 are the parameters of the normaldistribution. __________
8. The tails of the normal curve extend to infinity in bothdirections and theoretically never touch the vertical axis.__________
9. Because the distribution is symmetric, the area under thecurve to the left of the mean is .50 and the area under thecurve to the right of the mean is 1. __________
10. The standard normal distribution of a random variablehas a mean of zero and a standard deviation of 2.__________
11. If the value of 𝑥 is equal to 𝜇 , then its 𝑧 value is equal tozero. __________
12. For a normal distribution curve, the 𝑧 value for an 𝑥 valuethat is less than 𝜇 is always negative. __________
EXERCISE 2
Problem Solving. Answer what is required in the following problems.
A. Find the area of the following under the standard normal curve.
13. To the right of 𝑧 = 1.45
14. To the right of 𝑧 = −2.12
15. To the left of 𝑧 = −1.57
16. To the left of 𝑧 = 0.79
17. From 𝑧 = 0 and 𝑧 = 2.66
18. From 𝑧 = −1.36 and 𝑧 = 1.89
19. Between 𝑧 = 0 and 𝑧 = −2.96
20. Between 𝑧 = −0.25 and 𝑧 = −2.58
B. Assuming that 𝑧 is a standard normal random variable, find 𝑧for each of these cases.
21. The area to the left of 𝑧 is 0.7486
22. The area to the left of 𝑧 is 0.0951
23. The area to the right of 𝑧 is 0.1314
24. The area between 0 and 𝑧 is 0.4750.
25. The area to the right of 𝑧 is 0.2090
C. Draw a graph for the standard normal distribution. Label thehorizontal axis at values of −3,−2,−1, 0, 1, 2, and 3. Then use thetable of probabilities for the standard normal distribution tocompute the following probabilities.
26. 𝑃(𝑧 > −2.28)
27. 𝑃(𝑧 < −1.17)
28. 𝑃(𝑧 ≤ 1.24)
29. 𝑃(𝑧 ≥ −1.18)
30. 𝑃(−1.58 ≤ 𝑧 ≤ 0)
1
Economic Table is an economic model first describedby William Petty in 1759 laid the foundation of thePhysiocrats’ economic theories. ________
Republic of the Philippines Pangasinan State University
Lingayen Campu.s
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D. Determine the 𝑧 value for each of the following 𝑥 values for anormal distribution with 𝜇 = 60 and 𝜎 = 10.
31. 𝑥 = 45
32. 𝑥 = 60
33. 𝑥 = 82
34. 𝑥 = 33
35. 𝑥 = 51
E. Find the following areas under a normal distribution curve with𝜇 = 40 and 𝜎 = 8.
36. To the right of 𝑥 = 48
37. To the right of 𝑥 = 27
38. To the left of 𝑥 = 18
39. Between 𝑥 = 40 and 𝑥 = 55
40. Between 𝑥 = 16 and 𝑥 = 34
EXERCISE 3
Problem Analysis. Analyze and answer what is required in the following application problems.
A. According to a 2013 survey conducted by the marketing divisionof a telecommunication company, Filipino employees spend anaverage of 190 minutes per day communicating electronically (ona fixed landline phone, on a mobile phone, by emailing, by texting,and so on). Assume that currently such times for all Filipinoemployees are normally distributed with a mean of 190 minutesper day and a standard deviation of 21 minutes per day. Whatpercentage of Filipino employees communicate electronically for
41. Less than 150 minutes per day.
42. More than 235 minutes per day.
43. Between 130 and 180 minutes per day.
44. Between 180 and 240 minutes per day.
B. A fastfood restaurant claims that customers spend an averageof P174 on value meals with a standard deviation of P44. Assumethat the expenses incurred on meals by all such customers at thisrestaurant are normally distributed.
45. Find the probability that a randomly selected customerspends less than P212 on value meals.
46. What percentage of customers spend between P80 andP160 on value meals?
47. What percentage of customers spend between P140and P210?
48. Is it possible for a customer to spend more than P370on value meals? Explain.
C. The trading volume on the Philippine Stock Exchange isheaviest during the first half hour (early morning) and last halfhour (late afternoon) of the trading day. The early morning tradingvolumes (millions of shares) for 15 days in July 2014 are depictedbelow.
325 289 287 345 254 349 311 317 268 290 311 328 336 301 304 273
The probability distribution of trading volume is approximately normal.
49. Caculate the mean and standard deviation to use asestimates of the population mean and standarddeviation.
50. What is the probability that, on a randomly selected day,the early morning trading volume will be less than 245million shares?
51. What is the probability that, on a randomly selected day,the early morning trading volume will exceed 324 millionshares?
52. What is the probability that, on a randomly selected day,the early morning trading volume will be between 275and 310 million shares?
53. How many shares would have to be traded for the earlymorning trading volume on a particular day to be amongthe busiest 5% of days?
D. A study reports that the average monthly expenditure on foodfor all families in a particular city is P11,400. Assume that annualexpenditure on food is normally distributed and that the standarddeviation is P3,000.
54. What is the range of expenditures of the 10% of familieswith the lowest annual spending on food?
55. What percentage of families spend more than P14,000monthly on food?
56. What percentage of families spend less than P9,800monthly on food?
57. What is the probability that families spend betweenP7,000 and P12,000 monthly on food?
58. What is the range of expenditures for the 5% of familieswith the highest annual spending on food and drink?
E. The management of a department store wants to initiate a newpromotional campaign of giving a freebie to every customer whospends more than a certain amount per visit at this store. Themanagement expects that after this promotional campaign isadvertised, the expenditures for all customers at this store will benormally distributed with a mean of P845 and a standarddeviation of P270. What percentage of the customers areexpected to get freebies
59. If the management chooses to give freebies to all thosecustomers who spend more than P920 at thedepartment store during a visit?
60. If the management chooses to give freebies to all thosecustomers who spend less than P770 at the departmentstore during a visit?
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C. Suppose that 80 smartphone users are asked to name their favorite smartphone brand. The table below summarizes their responses. Note that these frequencies add up to 72. The remaining respondents named other brands, which can be denoted by “Others”.
23. Draw a pie chart for this distribution.
24. Based on the table, what is the most favorite smartphone
brand? What is its percentage share?
25. What is the percentage share of smartphone users who said that Nokia is their favorite brand?
26. What is the percentage share of smartphone users who said that Lenovo is their favorite brand?
D. Suppose the table below indicates the budget allocation of the Philippine government by department in 2012.
Budget Allocation
Millions of Pesos
Department of Education 238,800 Department of Public Works and Highways 126,400 Department of National Defense 108,100 Department of Interior and Local Government
99,800
Department of Agriculture 61,400 Department of Social Welfare and Development
48,800
Department of Health 45,800 Department of Transportation and Communications
34,700
State Universities and Colleges 25,800 Department of Finance 23,600 Department of Environment and Natural Resources
17,500
27. Draw a bar graph for this distribution.
E. The table below gives the frequency distribution of times (to the nearest hour) that selected 100 fans spent waiting in line to buy tickets to a rock concert. Find the following.
Waiting Time (hours) Frequency
0 to 6 14 7 to 13 27 14 to 20 31 21 to 27 21 28 to 34 7
28. The number of classes in the table is __________.
29. The class width is __________.
30. The midpoint of the third class is ___________.
31. The lower boundary of the second class is
____________.
32. The upper limit of the second class is ____________.
33. The sample size is __________.
34. The relative frequency of the second class is ___________.
F. A sample of 90 women was taken, and these women were asked about the number of shoes they possess. The following table provides the frequency distribution of their responses.
Number of Shoes
Number of Women
0 to 3 24 4 to 7 30
8 to 11 18 12 to 15 11 16 to 19 5 20 to 22 2
35. Find the class boundaries and class midpoints.
36. Do all classes have the same width? If so, what is this
width?
37. Prepare the relative frequency and percentage distribution columns.
38. What percentage of these women possess 8 or more
shoes? G. The following table gives the frequency distribution of ages for all 75 employees of a company.
Age Number of Teachers
21 to 30 17 31 to 40 25 41 to 50 18 51 to 60 15
39. Find the class boundaries and class midpoints.
40. Do all classes have the same width? If yes, what is that
width?
41. Prepare the relative frequency and percentage distribution columns.
42. What percentage of the teachers are age 43 or younger?
Favorite Smartphone
Frequency
Iphone 18 Samsung 28 HTC 4 Nokia 9 Blackberry 6 Lenovo 4 Alcatel 3
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H. JNE Panciteria makes pancit malabon. The following data are the numbers of bilaos produced at the panciteria for a sample of 30 days.
21 34 29 33 34 40 19 36 37 32 42 22 21 28 35 40 16 30 35 39 17 45 31 31 25 28 22 28 41 40
43. Construct a frequency distribution table using the classes
16–20, 21–25, 26–30, 31–35, 36–40 and 41–45.
44. Calculate the relative frequencies and percentages for all classes.
45. Construct a histogram and a polygon for the percentage
distribution.
46. For what percentage of the days is the number of pancit guisado produced in the interval 31–35?
I. The following data give the numbers of cellphone units owned by 36 randomly selected households.
3 3 6 1 5 2 1 4 2 2 3 1 2 3 2 2 6 5 0 5 5 6 0 1 5 5 3 2 3 2 4 2 3 3 6 4
47. Prepare a frequency distribution table for these data
using single-valued classes.
48. Compute the relative frequency and percentage distributions.
49. Draw a bar graph for the frequency distribution.
50. What percentage of the households own three or more
cellphones? J. The following tables gives the frequency distribution of the number of Smart TVs distributed by an electronics company to 70 local dealers.
No. of Smart TVs Number of Dealers
1 to 4 8 5 to 8 14 9 to 12 19 13 to 16 12 20 to 24 7 25 to 28 10
51. Prepare a cumulative frequency distribution.
52. Calculate the cumulative relative frequencies and
cumulative percentages for all classes.
53. Find the percentage of these dealers who ordered 12 or fewer smart TVs.
54. Draw an ogive for the cumulative percentage distribution.
55. Using the ogive, find the percentage of adults who
ordered 16 or higher smart TVs.
REFERENCES
Anderson, David et al. STATISTICS FOR BUSINESS AND ECONOMICS, 10th Edition. ThomsonSouth-Western. Mason, USA. 2012
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Calmorin, Laurentina P. RESEARCH AND STATISTICS WITH COMPUTER National Book StoreMandaluyong City 2010
Danao, Rolando A. INTRODUCTION TO STATISTICS AND ECONOMETRICS 1st Edition. QuezonCity Philippines, University of the Philippines Press, 2002.
Downie, N.M. & Health, R.W. BASIC STATISTICAL METHODS. Harper & Row Publishers, Inc.,N.Y.1997
Gravetter, Frederick and Wallnau, Larry. ESSENTIALS OF STATISTICS FOR THE BEHAVIORALSCIENCES, 8th EDITION. Wadsworth Cengage Learning, Belmont, USA. 2014.
Keller, Gerald STATISTICS FOR ECONOMICS AND MANAGEMENT, Phil. Ed. Cengage LearningAsia Pte. Ltd., Pasig City, Philippines, 2012
Mann, Prem S. INTRODUCTORY STATISTICS, 7TH EDITION. John Wiley and Sons, Inc. USA.2010
Mason, Robert D., et. al. STATISTICAL TECHNIQUES IN BUSINESS & ECONOMICS. TheMcGraw-Hills Companies, Inc., 1999.
Salvatore, Dominick. STATISTICS AND ECONOMETRICS 2nd Edition. USA, McGraw-Hill Education,2002
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