# Question

The Dow Jones Travel Index reported what business travelers pay for hotel rooms per night in major U.S. cities (The Wall Street Journal, January 16, 2004). The average hotel room rates for 20 cities are as follows:

a. What is the mean hotel room rate?

b. What is the median hotel room rate?

c. What is the mode?

d. What is the first quartile?

e. What is the third quartile?

6. During the 2007-2008 NCAA college basketball season, men's basketball teams attempted an all-time high number of 3-point shots, averaging 19.07 shots per game (Associated Press Sports, January 24, 2009). In an attempt to discourage so many 3-point shots and encourage more inside play, the NCAA rules committee moved the 3-point line back from 19 feet, 9 inches to 20 feet, 9 inches at the beginning of the 2008-2009 basketball season.

Shown in the following table are the 3-point shots taken and the 3-point shots made for a sample of 19 NCAA basketball games during the 2008-2009 season.

8. The cost of consumer purchases such as single-family housing, gasoline, Internet services, tax preparation, and hospitalization were provided in The Wall-Street Journal (January 2, 2007). Sample data typical of the cost of tax-return preparation by services such as H&R Block are shown below.

a. Compute the mean, median, and mode.

b. Compute the first and third quartiles.

c. Compute and interpret the 90th percentile.

9. The National Association of Realtors provided data showing that home sales were the slowest in 10 years (Associated Press, December 24, 2008). Sample data with representative sales prices for existing homes and new homes follow. Data are in thousands of dollars:

a. What is the median sales price for existing homes?

b. What is the median sales price for new homes?

c. Do existing homes or new homes have the higher median sales price? What is the difference between the median sales prices?

d. A year earlier the median sales price for existing homes was $208.4 thousand and the median sales price for new homes was $249 thousand. Compute the percentage change in the median sales price of existing and new homes over the one-year period.

Did existing homes or new homes have the larger percentage change in median sales price?

12. Walt Disney Company bought Pixar Animation Studios, Inc., in a deal worth $7.4 billion (CNN Money website, January 24, 2006). The animated movies produced by Disney and Pixar during the previous 10 years are listed in the following table. The box office revenues are in millions of dollars. Compute the total revenue, the mean, the median, and the quartiles to compare the box office success of the movies produced by both companies.

Do the statistics suggest at least one of the reasons Disney was interested in buying Pixar? Discuss.

17. A home theater in a box is the easiest and cheapest way to provide surround sound for a home entertainment center. A sample of prices is shown here (Consumer Reports Buying Guide, 2004). The prices are for models with a DVD player and for models without a DVD player.

a. Compute the mean price for models with a DVD player and the mean price for models without a DVD player. What is the additional price paid to have a DVD player included in a home theater unit?

b. Compute the range, variance, and standard deviation for the two samples. What does this information tell you about the prices for models with and without a DVD player?

18. Car rental rates per day for a sample of seven Eastern U.S. cities are as follows (The Wall Street Journal, January 16, 2004).

City Daily Rate

Boston .......... $43

Atlanta .......... 35

Miami ........... 34

New York .......... 58

Orlando .......... 30

Pittsburgh .......... 30

Washington, D.C. ....... 36

a. Compute the mean, variance, and standard deviation for the car rental rates.

b. A similar sample of seven Western U.S. cities showed a sample mean car rental rate of $38 per day. The variance and standard deviation were 12.3 and 3.5, respectively.

Discuss any difference between the car rental rates in Eastern and Western U.S. cities.

21. How do grocery costs compare across the country? Using a market basket of 10 items including meat, milk, bread, eggs, coffee, potatoes, cereal, and orange juice, Where to Retire magazine calculated the cost of the market basket in six cities and in six retirement areas across the country (Where to Retire, November/December 2003). The data with market basket cost to the nearest dollar are as follows:

a. Compute the mean, variance, and standard deviation for the sample of cities and the sample of retirement areas.

b. What observations can be made based on the two samples?

22. The National Retail Federation reported that college freshman spend more on back-to-school items than any other college group (USA Today, August 4, 2006). Sample data comparing the back-to-school expenditures for 25 freshmen and 20 seniors are shown in the data file BackToSchool.

a. What is the mean back-to-school expenditure for each group? Are the data consistent with the National Retail Federation's report?

b. What is the range for the expenditures in each group?

c. What is the interquartile range for the expenditures in each group?

d. What is the standard deviation for expenditures in each group?

e. Do freshmen or seniors have more variation in back-to-school expenditures?

27. Consider a sample with a mean of 30 and a standard deviation of 5. Use Chebyshev’s theorem to determine the percentage of the data within each of the following ranges:

a. 20 to 40

b. 15 to 45

c. 22 to 38

d. 18 to 42

e. 12 to 48

28. Suppose the data have a bell-shaped distribution with a mean of 30 and a standard deviation of 5. Use the empirical rule to determine the percentage of data within each of the following ranges:

a. 20 to 40

b. 15 to 45

c. 25 to 35

32. The high costs in the California real estate market have caused families who cannot afford to buy bigger homes to consider backyard sheds as an alternative form of housing expansion. Many are using the backyard structures for home offices, art studios, and hobby areas as well as for additional storage. The mean price of a customized wooden, shingled backyard structure is $3100 (Newsweek, September 29, 2003). Assume that the standard deviation is $1200.

a. What is the z-score for a backyard structure costing $2300?

b. What is the z-score for a backyard structure costing $4900?

c. Interpret the z-scores in parts (a) and (b). Comment on whether either should be considered an outlier.

d. The Newsweek article described a backyard shed-office combination built in Albany, California, for $13,000. Should this structure be considered an outlier? Explain.

35. Consumer Reports posts reviews and ratings of a variety of products on its website. The following is a sample of 20 speaker systems and their ratings. The ratings are on a scale of 1 to 5, with 5 being best.

a. Compute the mean and the median.

b. Compute the first and third quartiles.

c. Compute the standard deviation.

d. The skewness of this data is – 1.67. Comment on the shape of the distribution.

e. What are the z-scores associated with Allison One and Omni Audio?

f. Do the data contain any outliers? Explain.

38. Show the five-number summary and the box plot for the following data: 5, 15, 18, 10, 8, 12, 16, 10, 6.

44. A listing of 46 mutual funds and their 12-month total return percentage is shown in

Table 3.5 (Smart Money, February 2004).

a. What are the mean and median return percentages for these mutual funds?

b. What are the first and third quartiles?

c. Provide a five-number summary.

d. Do the data contain any outliers? Show a box plot.

47. Nielsen Media Research provides two measures of the television viewing audience: a television program rating, which is the percentage of households with televisions watching a program, and a television program share, which is the percentage of households watching a program among those with televisions in use. The following data show the Nielsen television ratings and share data for the Major League Baseball World Series over a nine-year period (Associated Press, October 27, 2003).

a. Develop a scatter diagram with rating on the horizontal axis.

b. What is the relationship between rating and share? Explain.

c. Compute and interpret the sample covariance.

d. Compute the sample correlation coefficient. What does this value tell us about the relationship between rating and share?

53. Consider the sample data in the following frequency distribution.

a. Compute the sample mean.

b. Compute the sample variance and sample standard deviation.

54. The grade point average for college students is based on a weighted mean computation.

For most colleges, the grades are given the following data values: A (4), B (3), C (2), D (1), and F (0). After 60 credit hours of course work, a student at State University earned 9 credit hours of A, 15 credit hours of B, 33 credit hours of C, and 3 credit hours of D.

a. Compute the student's grade point average.

b. Students at State University must maintain a 2.5 grade point average for their first 60 credit hours of course work in order to be admitted to the business college. Will this student be admitted?

57. The following frequency distribution shows the price per share of the 30 companies in the Dow Jones Industrial Average (Barron's, February 2, 2009).

a. Compute the mean price per share and the standard deviation of the price per share for the Dow Jones Industrial Average companies.

b. On January 16, 2006, the mean price per share was $45.83 and the standard deviation was $18.14. Comment on the changes in the price per share over the three-year period.

58. According to an annual consumer spending survey, the average monthly Bank of America Visa credit card charge was $1838 (U.S. Airways Attaché Magazine, December 2003). A sample of monthly credit card charges provides the following data.

a. Compute the mean and median.

b. Compute the first and third quartiles.

c. Compute the range and interquartile range.

d. Compute the variance and standard deviation.

e. The skewness measure for these data is 2.12. Comment on the shape of this distribution.

Is it the shape you would expect? Why or why not?

f. Do the data contain outliers?

59. The U.S. Census Bureau provides statistics on family life in the United States, including the age at the time of first marriage, current marital status, and size of household (U.S. Census Bureau website, March 20, 2006). The following data show the age at the time of first marriage for a sample of men and a sample of women.

a. Determine the median age at the time of first marriage for men and women.

b. Compute the first and third quartiles for both men and women.

c. Twenty-five years ago the median age at the time of first marriage was 25 for men and 22 for women. What insight does this information provide about the decision of when to marry among young people today?

60. Dividend yield is the annual dividend per share a company pays divided by the current market price per share expressed as a percentage. A sample of 10 large companies provided the following dividend yield data (The Wall Street Journal, January 16, 2004).

a. What are the mean and median dividend yields?

b. What are the variance and standard deviation?

c. Which company provides the highest dividend yield?

d. What is the z-score for McDonald’s? Interpret this z-score.

e. What is the z-score for General Motors? Interpret this z-score.

f. Based on z-scores, do the data contain any outliers?

61. The U.S. Department of Education reports that about 50% of all college students use a student loan to help cover college expenses (National Center for Educational Studies, January 2006). A sample of students who graduated with student loan debt is shown here.

The data, in thousands of dollars, show typical amounts of debt upon graduation.

a. For those students who use a student loan, what is the mean loan debt upon graduation?

b. What is the variance? Standard deviation?

62. Small business owners often look to payroll service companies to handle their employee payroll. Reasons are that small business owners face complicated tax regulations and penalties for employment tax errors are costly. According to the Internal Revenue Service, 26% of all small business employment tax returns contained errors that resulted in a tax penalty to the owner (The Wall Street Journal, January 30, 2006). The tax penalty for a sample of 20 small business owners follows:

a. What is the mean tax penalty for improperly filed employment tax returns?

b. What is the standard deviation?

c. Is the highest penalty, $2040, an outlier?

d. What are some of the advantages of a small business owner hiring a payroll service company to handle employee payroll services, including the employment tax returns?

64. The National Association of Realtors reported the median home price in the United States and the increase in median home price over a five-year period (The Wall Street Journal, January 16, 2006). Use the sample home prices shown here to answer the following questions.

a. What is the sample median home price?

b. In January 2001, the National Association of Realtors reported a median home price of $139,300 in the United States. What was the percentage increase in the median home price over the five-year period?

c. What are the first quartile and the third quartile for the sample data?

d. Provide a five-number summary for the home prices.

e. Do the data contain any outliers?

f. What is the mean home price for the sample? Why does the National Association of Realtors prefer to use the median home price in its reports?

a. What is the mean hotel room rate?

b. What is the median hotel room rate?

c. What is the mode?

d. What is the first quartile?

e. What is the third quartile?

6. During the 2007-2008 NCAA college basketball season, men's basketball teams attempted an all-time high number of 3-point shots, averaging 19.07 shots per game (Associated Press Sports, January 24, 2009). In an attempt to discourage so many 3-point shots and encourage more inside play, the NCAA rules committee moved the 3-point line back from 19 feet, 9 inches to 20 feet, 9 inches at the beginning of the 2008-2009 basketball season.

Shown in the following table are the 3-point shots taken and the 3-point shots made for a sample of 19 NCAA basketball games during the 2008-2009 season.

8. The cost of consumer purchases such as single-family housing, gasoline, Internet services, tax preparation, and hospitalization were provided in The Wall-Street Journal (January 2, 2007). Sample data typical of the cost of tax-return preparation by services such as H&R Block are shown below.

a. Compute the mean, median, and mode.

b. Compute the first and third quartiles.

c. Compute and interpret the 90th percentile.

9. The National Association of Realtors provided data showing that home sales were the slowest in 10 years (Associated Press, December 24, 2008). Sample data with representative sales prices for existing homes and new homes follow. Data are in thousands of dollars:

a. What is the median sales price for existing homes?

b. What is the median sales price for new homes?

c. Do existing homes or new homes have the higher median sales price? What is the difference between the median sales prices?

d. A year earlier the median sales price for existing homes was $208.4 thousand and the median sales price for new homes was $249 thousand. Compute the percentage change in the median sales price of existing and new homes over the one-year period.

Did existing homes or new homes have the larger percentage change in median sales price?

12. Walt Disney Company bought Pixar Animation Studios, Inc., in a deal worth $7.4 billion (CNN Money website, January 24, 2006). The animated movies produced by Disney and Pixar during the previous 10 years are listed in the following table. The box office revenues are in millions of dollars. Compute the total revenue, the mean, the median, and the quartiles to compare the box office success of the movies produced by both companies.

Do the statistics suggest at least one of the reasons Disney was interested in buying Pixar? Discuss.

17. A home theater in a box is the easiest and cheapest way to provide surround sound for a home entertainment center. A sample of prices is shown here (Consumer Reports Buying Guide, 2004). The prices are for models with a DVD player and for models without a DVD player.

a. Compute the mean price for models with a DVD player and the mean price for models without a DVD player. What is the additional price paid to have a DVD player included in a home theater unit?

b. Compute the range, variance, and standard deviation for the two samples. What does this information tell you about the prices for models with and without a DVD player?

18. Car rental rates per day for a sample of seven Eastern U.S. cities are as follows (The Wall Street Journal, January 16, 2004).

City Daily Rate

Boston .......... $43

Atlanta .......... 35

Miami ........... 34

New York .......... 58

Orlando .......... 30

Pittsburgh .......... 30

Washington, D.C. ....... 36

a. Compute the mean, variance, and standard deviation for the car rental rates.

b. A similar sample of seven Western U.S. cities showed a sample mean car rental rate of $38 per day. The variance and standard deviation were 12.3 and 3.5, respectively.

Discuss any difference between the car rental rates in Eastern and Western U.S. cities.

21. How do grocery costs compare across the country? Using a market basket of 10 items including meat, milk, bread, eggs, coffee, potatoes, cereal, and orange juice, Where to Retire magazine calculated the cost of the market basket in six cities and in six retirement areas across the country (Where to Retire, November/December 2003). The data with market basket cost to the nearest dollar are as follows:

a. Compute the mean, variance, and standard deviation for the sample of cities and the sample of retirement areas.

b. What observations can be made based on the two samples?

22. The National Retail Federation reported that college freshman spend more on back-to-school items than any other college group (USA Today, August 4, 2006). Sample data comparing the back-to-school expenditures for 25 freshmen and 20 seniors are shown in the data file BackToSchool.

a. What is the mean back-to-school expenditure for each group? Are the data consistent with the National Retail Federation's report?

b. What is the range for the expenditures in each group?

c. What is the interquartile range for the expenditures in each group?

d. What is the standard deviation for expenditures in each group?

e. Do freshmen or seniors have more variation in back-to-school expenditures?

27. Consider a sample with a mean of 30 and a standard deviation of 5. Use Chebyshev’s theorem to determine the percentage of the data within each of the following ranges:

a. 20 to 40

b. 15 to 45

c. 22 to 38

d. 18 to 42

e. 12 to 48

28. Suppose the data have a bell-shaped distribution with a mean of 30 and a standard deviation of 5. Use the empirical rule to determine the percentage of data within each of the following ranges:

a. 20 to 40

b. 15 to 45

c. 25 to 35

32. The high costs in the California real estate market have caused families who cannot afford to buy bigger homes to consider backyard sheds as an alternative form of housing expansion. Many are using the backyard structures for home offices, art studios, and hobby areas as well as for additional storage. The mean price of a customized wooden, shingled backyard structure is $3100 (Newsweek, September 29, 2003). Assume that the standard deviation is $1200.

a. What is the z-score for a backyard structure costing $2300?

b. What is the z-score for a backyard structure costing $4900?

c. Interpret the z-scores in parts (a) and (b). Comment on whether either should be considered an outlier.

d. The Newsweek article described a backyard shed-office combination built in Albany, California, for $13,000. Should this structure be considered an outlier? Explain.

35. Consumer Reports posts reviews and ratings of a variety of products on its website. The following is a sample of 20 speaker systems and their ratings. The ratings are on a scale of 1 to 5, with 5 being best.

a. Compute the mean and the median.

b. Compute the first and third quartiles.

c. Compute the standard deviation.

d. The skewness of this data is – 1.67. Comment on the shape of the distribution.

e. What are the z-scores associated with Allison One and Omni Audio?

f. Do the data contain any outliers? Explain.

38. Show the five-number summary and the box plot for the following data: 5, 15, 18, 10, 8, 12, 16, 10, 6.

44. A listing of 46 mutual funds and their 12-month total return percentage is shown in

Table 3.5 (Smart Money, February 2004).

a. What are the mean and median return percentages for these mutual funds?

b. What are the first and third quartiles?

c. Provide a five-number summary.

d. Do the data contain any outliers? Show a box plot.

47. Nielsen Media Research provides two measures of the television viewing audience: a television program rating, which is the percentage of households with televisions watching a program, and a television program share, which is the percentage of households watching a program among those with televisions in use. The following data show the Nielsen television ratings and share data for the Major League Baseball World Series over a nine-year period (Associated Press, October 27, 2003).

a. Develop a scatter diagram with rating on the horizontal axis.

b. What is the relationship between rating and share? Explain.

c. Compute and interpret the sample covariance.

d. Compute the sample correlation coefficient. What does this value tell us about the relationship between rating and share?

53. Consider the sample data in the following frequency distribution.

a. Compute the sample mean.

b. Compute the sample variance and sample standard deviation.

54. The grade point average for college students is based on a weighted mean computation.

For most colleges, the grades are given the following data values: A (4), B (3), C (2), D (1), and F (0). After 60 credit hours of course work, a student at State University earned 9 credit hours of A, 15 credit hours of B, 33 credit hours of C, and 3 credit hours of D.

a. Compute the student's grade point average.

b. Students at State University must maintain a 2.5 grade point average for their first 60 credit hours of course work in order to be admitted to the business college. Will this student be admitted?

57. The following frequency distribution shows the price per share of the 30 companies in the Dow Jones Industrial Average (Barron's, February 2, 2009).

a. Compute the mean price per share and the standard deviation of the price per share for the Dow Jones Industrial Average companies.

b. On January 16, 2006, the mean price per share was $45.83 and the standard deviation was $18.14. Comment on the changes in the price per share over the three-year period.

58. According to an annual consumer spending survey, the average monthly Bank of America Visa credit card charge was $1838 (U.S. Airways Attaché Magazine, December 2003). A sample of monthly credit card charges provides the following data.

a. Compute the mean and median.

b. Compute the first and third quartiles.

c. Compute the range and interquartile range.

d. Compute the variance and standard deviation.

e. The skewness measure for these data is 2.12. Comment on the shape of this distribution.

Is it the shape you would expect? Why or why not?

f. Do the data contain outliers?

59. The U.S. Census Bureau provides statistics on family life in the United States, including the age at the time of first marriage, current marital status, and size of household (U.S. Census Bureau website, March 20, 2006). The following data show the age at the time of first marriage for a sample of men and a sample of women.

a. Determine the median age at the time of first marriage for men and women.

b. Compute the first and third quartiles for both men and women.

c. Twenty-five years ago the median age at the time of first marriage was 25 for men and 22 for women. What insight does this information provide about the decision of when to marry among young people today?

60. Dividend yield is the annual dividend per share a company pays divided by the current market price per share expressed as a percentage. A sample of 10 large companies provided the following dividend yield data (The Wall Street Journal, January 16, 2004).

a. What are the mean and median dividend yields?

b. What are the variance and standard deviation?

c. Which company provides the highest dividend yield?

d. What is the z-score for McDonald’s? Interpret this z-score.

e. What is the z-score for General Motors? Interpret this z-score.

f. Based on z-scores, do the data contain any outliers?

61. The U.S. Department of Education reports that about 50% of all college students use a student loan to help cover college expenses (National Center for Educational Studies, January 2006). A sample of students who graduated with student loan debt is shown here.

The data, in thousands of dollars, show typical amounts of debt upon graduation.

a. For those students who use a student loan, what is the mean loan debt upon graduation?

b. What is the variance? Standard deviation?

62. Small business owners often look to payroll service companies to handle their employee payroll. Reasons are that small business owners face complicated tax regulations and penalties for employment tax errors are costly. According to the Internal Revenue Service, 26% of all small business employment tax returns contained errors that resulted in a tax penalty to the owner (The Wall Street Journal, January 30, 2006). The tax penalty for a sample of 20 small business owners follows:

a. What is the mean tax penalty for improperly filed employment tax returns?

b. What is the standard deviation?

c. Is the highest penalty, $2040, an outlier?

d. What are some of the advantages of a small business owner hiring a payroll service company to handle employee payroll services, including the employment tax returns?

64. The National Association of Realtors reported the median home price in the United States and the increase in median home price over a five-year period (The Wall Street Journal, January 16, 2006). Use the sample home prices shown here to answer the following questions.

a. What is the sample median home price?

b. In January 2001, the National Association of Realtors reported a median home price of $139,300 in the United States. What was the percentage increase in the median home price over the five-year period?

c. What are the first quartile and the third quartile for the sample data?

d. Provide a five-number summary for the home prices.

e. Do the data contain any outliers?

f. What is the mean home price for the sample? Why does the National Association of Realtors prefer to use the median home price in its reports?

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