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Solution Manual for Statistics for Business and Economics, 11th Edition

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    Solutions Manual to Accompany Statistics for Business and Economics Eleventh Edition David R. Anderson University of Cincinnati Dennis J. Sweeney University of Cincinnati Thomas A. Williams Rochester Institute of Technology

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    Contents Chapter 1. Data and Statistics 2. Descriptive Statistics: Tabular and Graphical Presentations 3. Descriptive Statistics: Numerical Me asures 4. Introduction to Probability 5. Discrete Probability Distributions 6. Continuous Probability Distributions 7. Sampling and Sampling Distributions 8. Interval Estimation 9. Hypothesis Testing 10. Statistical Inference about Means and Proportions With Two Populations 11. Inferences about Population Variances 12. Tests of Goodness of Fit and Independence 13. Experimental Design and Analysis of Variance 14. Simple Linear Regression 15. Multiple Regression 16. Regression Analysis: Model Building 17. Index Numbers 18. Time Series Analysis and Forecasting 19. Nonparametric Methods 20. Statistical Methods for Quality Control 21. Decision Analysis 22. Sample Survey

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    Preface The purpose of Statistics for Business and Economics is to provide students, primarily in the fields of business administration and economics, with a sound conceptual introduction to the field of statistics and its many applications. The text is applications - oriented and has been written with the needs of the nonmathematician in mind. The solutions manual furnishes assistance by identifying learning objectives and providing detailed solutions for all exercises in the text. Note: The solutions to the case problems are included in a separate manual. Acknowledgements We would like to provide special recognition to Catherine J. Williams for her efforts in preparing the solutions manual. David R. Anderson Dennis J. Sweeney Thomas A. Williams

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    1 - 1 Chapter 1 Data and Statistics Learning Objectives 1. Obtain an appreciation for the breadth of statistical applications in business and economics. 2. Understand the meaning of the terms elements, variables, and observations as they are used in statistics. 3. Obtain an understanding of the difference between categorical, quantitative, crossectional and time series data. 4. Learn about the sources of data for statistical analysis both internal and external to the firm. 5. Be aware of how errors can arise in data. 6. Know the meaning of descriptive statistics and statistical inference. 7. Be able to distinguish between a population and a sample. 8. Understand the role a sample plays in making statistical inferences about the population. 9. Know the meaning of the term data mining. 10. Be aware of ethical guidelines for statistical practice. Solutions:

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    Chapter 1 1 - 2 1. Statistics can be referred to as numerical facts. In a broader sense, statistics is the field of study dealing with the collection, analysis, presentation and interpretation of data. 2. a. The ten elements are the ten cars b. 5 variables: Size, Cylinders, City MPG, Highway MPG, and Fuel c. Categorical variables: Size and Fuel Quantitative variables: Cylinders, City MPG, and Highway MPG d. Variable Measurement Scale Size Ordinal Cylinders Ratio City MPG Ratio Highway MPG Ratio Fuel Nominal 3. a. Average mpg for city driving = 182/10 = 18.2 mpg b. Average mpg for highway driving = 261/10 = 26.1 mpg On average, the miles per gallon for highway driving is 26.1 – 18.2 = 7.9 mpg greater compared to city driving. c. 3 of 10 or 30% have four cylinder engines d. 6 of 10 or 6 0% use regular fuel 4. a. The seven elements are the seven schools shown b. 5 variables: State, Campus Setting, Endowment, Applicants Admitted, and NCAA Division c. Categorical variables: State, Campus Setting, and NCAA Division Quantitative variables: Endowment and Applicants Admitted 5. a. Average endowment = 74.6/7 = $10.657 billion b. Average percentage admitted = 111/7 = 15.86% c. 3 of 7 or 42.9% have NCAA Division III varsity teams d. 3 of 7 or 42.9% have a City: Midsize campus setting 6. a. Quantitative b. Categorical c. Categorical d. Quantitative

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    Data and Statistics 1 - 3 e. Categorical 7. a. Although the data are recorded as numbers, the numbers are codes for the ratings of Fair (1), Average (2), Good (3) and Excellent (4). Thus the variables are categorical with each data value corresponding to a rating category for the variable . b. The data may also be ranked in order of the quality. A higher number indicates a higher rating on a scale from Fair (1) to Excellent (4). Since the data can be ranked or ordered, the scale of measurement is ordinal. 8. a. 1015 b. Categorical c. Percentages d. .10(1015) = 101.5 101 or 102 respondents said the Federal Bank is doing a good job. 9. a. Categorical b. 30 of 71; 42.3% 10. a. Quantitative; ratio scale of measurement b. Categorical ; nominal scale of measurement c. Categorical ; ordinal scale of measurement since the responses can be ordered from earliest (high school) to latest (retirement) d. Quantitative; ratio scale of measurement e. Categorical ; nominal scale of measurement 11. a. Quantitative; ratio b. Categorical ; ordinal c. Categorical ; ordinal (assuming employees can be ranked by classification) d. Quantitative; ratio e. Categorical ; nominal 12. a. The population is all visitors coming to the state of Hawaii. b. Since airline flights carry the vast majority of visitors to the state , the use of questionnaires for passengers during incoming flights is a good way to reach this population. The questionnaire actually appears on the back of a mandatory plants and animals declaration form that passengers must complete during the incoming flight. A large percentage of passengers complete the visitor information questionnaire. c. Questions 1 and 4 provide quantitative data indicating the number of visits and the number of days in Hawaii. Questions 2 and 3 provide categorical data indicating the categories of reason for the trip and where the visitor plans to stay.

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    Chapter 1 1 - 4 13. a. Federal spending measured in trillions of dollars b. Quantitative c. Time series d. Federal spending has increased over time 1 4. a. 0 2 4 6 8 10 12 2003 2004 2005 2006 2007 2008 Year Vehicles (millions) Toyota GM Ford DC b. According to the CSM data, Toyota surpasses General Motors as the biggest auto manufacturer in the world in 2006. In 2006, Toyota manufactured approximately (9.1 – 8.9) = .2 million or 200,000 more vehicles than General Motors. The gap is expected to widen to 800,000 vehicles in 2007. General Motors is the only manufacturer showing a decline in vehicle production over the four year period. c. The following is a bar chart of cross - sectional data as it shows the number of v ehicles manufactured in 2007.

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    Data and Statistics 1 - 5 0 2 4 6 8 10 12 GM Ford DC Toyota Manufacturer Vehicles (millions) 15. a. Quantitative – number of new drugs approved b. Time series from 1996 to 2003 c. 18 d. 2002; 16 new drugs e. Over the eight - year period, the number of new drugs approved by the FDA declined. From approximately 50 new drugs approved in 1996, the most recent years are showing only 16 to 18 new drugs approved. 16. The answer to this exercise depends upon the time series of the average price per gallon of conventional regular gasoline since April 2009. Contact the website www.eia.doe.gov to obtain the more recent time series data. In the spring of 2009, the average price per gallon was once again increasing. A continuation of the usual summer peak in gasoline prices was anticipated. 17. Internal data on salaries of other employees can be obtained from the personnel department. External data might be obtained from the Department of Labor or industry associations. 18. a. 155 .36 430 = or 36% b. 44% of 430 = .44(430) = 189 business travelers c. Categorical data with categories online travel site, travel agent, direct with airline/hotel, other. 19. a. All subscribers of Business Week in North America at the time the survey was conducted. b. Quantitative c. Categorical (yes or no) d. Crossectional - all the data relate to the same time.

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    Chapter 1 1 - 6 e. Using the sample results, we could infer or estimate 59% of the population of subscribers have an annual income of $75,000 or more and 50% of the population of subscribers have an American Express credit card. 20. a. 43% of managers were bullish or very bullish. 21% of managers expected health care to be the leading industry over the next 12 months. b. We estimate the average 12 - month return estimate for the population of investment managers to be 11.2%. c. We estimate the average over the population of investment managers to be 2.5 years. 21. a. The two populations are the population of women whose mothers took the drug DES during pregnancy and the population of women whose mothers did not take the drug DES during pregnancy. b. It was a survey. c. 63 / 3.980 = 15.8 women out of each 1000 developed tissue abnormalities. d. The article reported “twice” as many abnormalities in the women whose mothers had taken DES during pregnancy. Thus, a rough estimate would be 15.8/2 = 7.9 abnormalities per 1000 women whose mothers had not taken DES during pregnancy. e. In many situations, disease occurrences are rare and affect only a small portion of the population. Large samples are needed to collect data on a reasonable number of cases where the disease exists. 22. a. The population consists of all customers of the chain’s stores in Charlotte, North Carolina. b. Some of the ways that could used to collect the data are as follows: • Customers entering or leaving the store could be surveyed • A survey could be mailed to customers who have a shopper’s club card for the stores • Customers could be given a printed survey when they check out • Customers could be given a coupon that asks them to complete a brief on - line survey; if they do, they will receive a 5% discount on their next shopping trip. 23. a. Nielsen is attempting to measure the popularity of each television program by showing the percentage of households that are watching the program. b. All households with televisions in the United States. c. A census of the population is impossible. A sample provides timely information in that the ratings and share data can be obtained weekly. In addition, the sample saves data collection costs. d. The cancellation or renewal of television programs, advertising cost rates for the television programs and the scheduling of television programs are often based on the Nielsen information. 24. a. This is a statistically correct descriptive statistic for the sample. b. An incorrect generalization since the data was not collected for the entire population. c. An acceptable statistical inference based on the use of the word “estimate.”

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    Data and Statistics 1 - 7 d. While this statement is true for the sample, it is not a justifiable conclusion for the entire population. e. This statement is not statistically supportable. While it is true for the particular sample observed, it is entirely possible and even very likely that at least some students will be outside the 65 to 90 range of grades. 25. a. T here are five variables: Exchange, Ticker Symbol, Market Cap, Price/Earnings Ratio and Gross Profit Margin. b. Categorical variables: Exchange and Ticker Symbol Quantitative variables: Market Cap, Price/Earnings Ratio, Gross Profit Margin c. Exchange variable: Exchange Frequency Percent Frequency AMEX 5 (5/25) 20% NYSE 3 (3/25) 12% OTC 17 (17/25) 68% 25 0 10 20 30 40 50 60 70 80 AMEX NYSE OTC Exchange Percent Frequency d. Gross Profit Margin variable: Gross Profit Margin Frequency 0.0 – 14.9 2 1 5.0 – 29.9 6 30.0 – 44.9 8 45 .0 – 59 .9 6 60 .0 – 74 .9 3

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    Chapter 1 1 - 8 0 1 2 3 4 5 6 7 8 9 0.0-14.9 15.0-29.9 30.0-44.9 45.0-59.9 60.0-74.9 Gross Profit Margin Frequency e. Sum the Price/Earnings Ratio data for all 25 companies. Sum = 505.4 Average Price/Earnings Ratio = Sum/25 = 505.4/25 = 20.2

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    2 - 1 Chapter 2 Descriptive Statistics: Tabular and Graphical Presentation s Learning Objectives 1. Learn how to construct and interpret summarization procedures for qualitative data such as: frequency and relative frequency distributions, bar graphs and pie charts. 2. Learn how to construct and interpret tabular summarization procedures for quantitative data such as: frequency and relative frequency distributions, cumulative frequency and cumulative relative frequency distributions. 3. Learn how to construct a dot plot, a histogram, and an ogive as graphical summaries of quantitative data. 4. Learn how the shape of a data distribution is revealed by a histogram. Learn how to recognize when a data distribution is negatively skewed, symmetric, and positively skewed. 5. Be able to use and interpret the exploratory data analysis technique of a stem - and - leaf display. 6. Learn how to construct and interpret cross tabulations and scatter diagrams of bivariate data.

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    Chapter 2 2 - 2 Solutions: 1. Class Frequency Relative Frequency A 60 60/120 = 0.50 B 24 24/120 = 0.20 C 36 36/120 = 0.30 120 1.00 2. a. 1 - (.22 + .18 + .40) = .20 b. .20(200) = 40 c/d. Class Frequency Percent Frequency A .22(200) = 44 22 B .18(200) = 36 18 C .40(200) = 80 40 D .20(200) = 40 20 Total 200 100 3. a. 360° x 58/120 = 174° b. 360° x 42/120 = 126° c. d. Yes 48.3% No Opinion 16.7% No 35.0%

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    Descriptive Statistics: Tabular and Graphical Presentation s 2 - 3 0 10 20 30 40 50 60 70 Yes No No Opinion Response Frequency 4. a. Categorical b. TV Show Frequency Percent Frequency Law & Order 10 20% CSI 18 36% Without a Trace 9 18% Desperate Housewives 13 26% Total: 50 100% 0 2 4 6 8 10 12 14 16 18 20 L&O CSI Trace Housewives TV Show Frequency

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    Chapter 2 2 - 4 d. CSI had the largest viewing audience. Desperate Housewives was in second place. 5. a. Name Frequency Relative Frequency Percent Frequency Brown 7 .14 14% Davis 6 .12 12% Johnson 10 .20 20% Jones 7 .14 14% Smith 12 .24 24% Williams 8 .16 16% 50 1.00 b. 0 2 4 6 8 10 12 14 Brown Davis Johnson Jones Smith Williams Name Frequency c. Brown .14 x 360 = 50.4  Davis .12 x 360 = 43.2  Johnson .20 x 360 = 72.0  Jones .14 x 360 = 50.4  Smith .24 x 360 = 86.4  Williams .16 x 360 = 57.6  L&O 20% CSI 36% Trace 18% Housewives 26%

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    Descriptive Statistics: Tabular and Graphical Presentation s 2 - 5 d. Most common: Smith, Johnson and Williams 6. a. Network Frequency Percent Frequency ABC 15 30% CBS 17 34% FOX 1 2% NBC 17 34% Total 50 100% 0 2 4 6 8 10 12 14 16 18 ABC CBS FOX NBC Network Frequency b. CBS and NBC are tied, each with 17 of the top rated television shows. ABC is a close third with 15. The fact that the three networks are so close is surprising. FOX, the newest television network, does not have the history to compete with the other three networks in term of the top rated shows in television history. Williams 16% Brown 14% Davis 12% Johnson 20% Jones 14% Smith 24%

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    Chapter 2 2 - 6 7. Rating Frequency Relative Frequency Outstanding 19 0.38 Very Good 13 0.26 Good 10 0.20 Average 6 0.12 Poor 2 0.04 50 1.00 Management should be pleased with these results. 64% of the ratings are very good to outstanding. 84% of the ratings are good or better. Comparing these ratings with previous results will show whether or not the restaurant is making improvements in its ratings of food quality. 8. a. Position Frequency Relative Frequency Pitcher 17 0.309 Catcher 4 0.073 1st Base 5 0.091 2nd Base 4 0.073 3rd Base 2 0.036 Shortstop 5 0.091 Left Field 6 0.109 Center Field 5 0.091 Right Field 7 0.127 55 1.000 b. Pitchers (Almost 31%) c. 3rd Base (3 - 4%) d. Right Field (Almost 13%) e. Infielders (16 or 29.1%) to Outfielders (18 or 32.7%) 9. a. b. Where do you live now? Living Area Live Now Ideal Community City 32% 24% Suburb 26% 25% Small Town 26% 30% Rural Area 16% 21% Total 100% 100%

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    Descriptive Statistics: Tabular and Graphical Presentation s 2 - 7 What do you consider the ideal community? c. Most adults are now living in a city (32%). d. Most adults consider the ideal community a small town (30%). e. Percent changes by living area: City - 8%, Suburb - 1%, Small Town +4%, and Rural Area +5%. Suburb living is steady, but the trend would be that living in the city would decline while living in small towns and rural areas would increase. 10. a. Rating Frequency Excellent 20 Good 101 Fair 528 Bad 244 Terrible 122 Total 1015 b.

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    Chapter 2 2 - 8 Rating Percent Frequency Excellent 2 Good 10 Fair 52 Bad 24 Terrible 12 Total 100 c. d. 24% + 12% = 36% of adults in the United Sates think the Federal Bank is doing a bad or a terrible job in handling the credit problems. Only 10% + 2% = 12% think the Federal Bank is doing a good or excellent job. e. 40% + 10% = 50% of adults in Spain think the European Central Bank is doing a bad or terrible job in handling the credit problems. Only 4% of adults in Spain think the European Central Bank is doing a good or excellent job. Both countries show pessimism and relatively low confidence in how the banks are handling the credit problems in the financial markets. But in comparing the two countries, adults in Spain show more concern and more pessimism about the bank’s ability compared to adults in the United States. 11. Class Frequency Relative Frequency Percent Frequency 12 - 14 2 0.050 5.0 15 - 17 8 0.200 20.0 18 - 20 11 0.275 27.5 21 - 23 10 0.250 25.0 24 - 26 9 0.225 22.5 Total 40 1.000 100.0 12. Class Cumulative Frequency Cumulative Relative Frequency

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    Descriptive Statistics: Tabular and Graphical Presentation s 2 - 9 less than or equal to 19 10 .20 less than or equal to 29 24 .48 less than or equal to 39 41 .82 less than or equal to 49 48 .96 less than or equal to 59 50 1.00 13. 0 2 4 6 8 10 12 14 16 18 10-19 20-29 30-39 40-49 50-59 Frequency .2 .4 .6 .8 0 10 20 30 40 50 1.0 60 14. a. b/c.

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    Chapter 2 2 - 10 Class Frequency Percent Frequency 6.0 - 7.9 4 20 8.0 - 9.9 2 10 10.0 - 11.9 8 40 12.0 - 13.9 3 15 14.0 - 15.9 3 15 20 100 15. a/b. Waiting Time Frequency Relative Frequency 0 - 4 4 0.20 5 - 9 8 0.40 10 - 14 5 0.25 15 - 19 2 0.10 20 - 24 1 0.05 Totals 20 1.00 c/d. Waiting Time Cumulative Frequency Cumulative Relative Frequency Less than or equal to 4 4 0.20 Less than or equal to 9 12 0.60 Less than or equal to 14 17 0.85 Less than or equal to 19 19 0.95 Less than or equal to 24 20 1.00 e. 12/20 = 0.60 16. a. Salary Frequency 150 - 159 1 160 - 169 3 170 - 179 7 180 - 189 5 190 - 199 1 200 - 209 2 210 - 219 1 Total 20 b. Salary Percent Frequency 150 - 159 5 160 - 169 15 170 - 179 35 180 - 189 25 190 - 199 5 200 - 209 10 210 - 219 5 Total 100 c. Salary Cumulative Percent Frequency

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    Descriptive Statistics: Tabular and Graphical Presentation s 2 - 11 Less than or equal to 159 5 Less than or equal to 169 20 Less than or equal to 179 55 Less than or equal to 189 80 Less than or equal to 199 85 Less than or equal to 209 95 Less than or equal to 219 100 Total 100 d. e. There is skewness to the right. f. (3/20)(100) = 15% 17. a. The highest price stock is for IBM with a price of $10 7 per share. The lowest price stock is for Alcoa with a price of $11 per share. b. A class size of 10 results in 10 classes. Price per Share Frequency $10 - 19 5 $20 - 29 10 $30 - 39 3 $40 - 49 2 $50 - 59 6 $60 - 69 2 $70 - 79 1 $80 - 89 0 $90 - 99 0 $100 - 109 1 c.

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    Chapter 2 2 - 12 The general shape of the distribution is skewed to the right. Half of the companies (15) have a price per share less than $30. A mid - priced stock appears to be in the $30 to $49 range, while the most frequently priced stock is in the $20 to $29 range. Five stocks are less than $20 per share (Alcoa, Bank of America, General Electric, Intel and Pfizer). Four stocks are $60 or more per share (3M, Chevron, ExxonMobil and IBM). d. A variety of comparisons are possible depending upon when the study is done. 18. a. The lowest holiday spending is $180; the highest $2050. b. Spending Frequency Percent 0 - 249 3 12 250 - 499 6 24 500 - 749 5 20 750 - 999 5 20 1000 - 1249 3 12 1250 - 1499 1 4 1500 - 1759 0 0 1750 - 1999 1 4 2000 - 2249 1 4 Total 25 100 c . The distribution shows a positive skewness.

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    Descriptive Statistics: Tabular and Graphical Presentation s 2 - 13 0 1 2 3 4 5 6 7 0-249 250-499 500-749 750-999 1000- 1249 1250- 1499 1500- 1759 1750- 1999 2000- 2249 Holiday Spending Frequency d. The holiday spending ranges from $0 to less than $2250. The majority of the spending is between $250 and $1000 with 16 of the 25 customers, 64%, in this range. The middle or average spending is around $750 per customer. The distribution has a positive skewness with two consumers above $1750. One consumer is above $2000. 19. a/b/c/d. Class (Minutes) Frequency Relative Frequency Cumulative Frequency Cumulative Relative Frequency 1 - 5 12 .60 12 .60 6 - 10 3 .15 15 .75 11 - 15 2 .10 17 .85 16 - 20 1 .05 18 .90 21 - 25 1 .05 19 .95 26 - 30 0 .00 19 .95 31 - 34 1 .05 20 1.00 e. f. 60% of office workers spend 5 minutes or less on unsolicited email and spam. However, 25% of office workers spend more than 10 minutes per day on this task. 20. a . Off - Course Income Percent 0 0.2 0.4 0.6 0.8 1 0 5 10 15 20 25 30 35 Time

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    Chapter 2 2 - 14 ( $1000 s) Frequency Frequency 0 - 4,999 30 60 5,000 - 9,999 9 18 10,000 - 14,999 4 8 15,000 - 19,999 0 0 20,000 - 24,999 3 6 25,000 - 29,999 2 4 30,000 - 34,999 0 0 35000 - 39,999 0 0 40,000 - 44,999 1 2 45,000 - 49,999 0 0 Over 50,000 1 2 Total 50 100 b. Histogram of Off - Course Income Note: The first class is labeled 5000 and provides the golfers who had an off - course income in the range 0 to 4999 or less than 5000. These were the golfers with less than $5 million in off - course income. c. Off - course income is skewed to the right. Only Tiger Woods earns over $50 million. d. Considering the top 50 golfers, the majority (60%) earn less than $5 million in off - course income per year. 60% + 18% = 78% earn less than $10 million. Five golfers (10%) earn between $20 million and $30 million. Tiger Woods with $99.8 million and Phil Mickelson with $40.2 million in off - course income are clearly the leaders in this income category. 21. a/b.

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    Descriptive Statistics: Tabular and Graphical Presentation s 2 - 15 Computer Usage (Hours) Frequency Relative Frequency 0.0 - 2.9 5 0.10 3.0 - 5.9 28 0.56 6.0 - 8.9 8 0.16 9.0 - 11.9 6 0.12 12.0 - 14.9 3 0.06 Total 50 1.00 c. 0 5 10 15 20 25 30 0-2.9 3-5.9 6-8.9 9-11.9 12-14.9 Computer Usage (Hours) Frequency d. e. The majority of the computer users are in the 3 to 6 hour range. Usage is somewhat skewed toward the right with 3 users in the 12 to 14.9 hour range. 2 2.

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    Chapter 2 2 - 16 5 7 8 6 4 5 8 7 0 2 2 5 5 6 8 8 0 2 3 5 23. Leaf Unit = .1 6 3 7 5 5 7 8 1 3 4 8 9 3 6 10 0 4 5 11 3 24. Leaf Unit = 10 11 6 12 0 2 13 0 6 7 14 2 2 7 15 5 16 0 2 8 17 0 2 3 25. 9 8 9 10 2 4 6 6 11 4 5 7 8 8 9 12 2 4 5 7 13 1 2 14 4 15 1 26. a. 100 shares at $50 per share

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    Descriptive Statistics: Tabular and Graphical Presentation s 2 - 17 1 0 3 7 7 2 4 5 5 3 0 0 5 5 9 4 0 0 0 5 5 8 5 0 0 0 4 5 5 This stem - and - leaf display shows that the trading prices are closely grouped together. Rotating the stem - and - leaf display counter clockwise shows a histogram that is slightly skewed to the left but is roughly symmetric. b. 500 shares traded online at $50 per share. 0 5 7 1 0 1 1 3 4 1 5 5 5 8 2 0 0 0 0 0 0 2 5 5 3 0 0 0 3 6 4 4 5 5 6 3 This stretched stem - and - leaf display shows that the distribution of online trading prices for most of the brokers for 500 shares are lower than the trading prices for broker assisted trades of 100 shares. There are a couple of outliers. York Securities charges $36 for an online trade and Investors National charges much more than the other brokers: $62.50 for an online trade. 27. a. 7 5 9 8 3 6 9 5 6 8 10 0 4 4 11 1 5 12 13 7 14 5 5 b. Observations such as the following can be made using the stem - and - leaf display.

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    Chapter 2 2 - 18 • The daily rate varies from $75 to $145 • Typical mid - priced daily rates are $95 to $115 with the average daily rate around $100. • A daily rate in excess of $115 should be considered relatively high. High daily rates of $137 and $145 were found at three ski resorts. 28. a. 2 1 4 2 6 7 3 0 1 1 1 2 3 3 5 6 7 7 4 0 0 3 3 3 3 3 4 4 4 6 6 7 9 5 0 0 0 2 2 5 5 6 7 9 6 1 4 6 6 7 2 b. Most frequent age group: 40 - 44 with 9 runners c. 43 was the most frequent age with 5 runners d. 4/40 = 10% of the runners were “20 - something.” With only 10% of the registrants “20 - something,” the article pointed out that surprisingly few registrants were in this age group. One suggested reason was that “20 - somethings” don’t have the time to train for a 13.1 mile race. For “20 - somethings,” college, starting careers, and starting families may take priority over training for long distance races. 29. a. y x A B C 5 11 2 0 2 10 12 18 5 13 12 30 Total 1 2 Total b.

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    Descriptive Statistics: Tabular and Graphical Presentation s 2 - 19 y x A B C 100.0 84.6 16.7 1 0.0 15.4 83.3 2 100.0 100.0 100.0 Total c. y x A B C 27.8 61.1 11.1 100.0 0.0 16.7 83.3 100.0 1 2 Total d. Category A values for x are always associated with category 1 values for y . Category B values for x are usually associated with category 1 values for y. Category C values for x are usually associated with category 2 values for y . 30. a. -40 -24 -8 8 24 40 56 -40 -30 -20 -10 0 10 20 30 40 x y b. There is a negative relationship between x and y; y decreases as x increases.

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