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5.2 Consider the random experiment of a worker assembling a product.
a. Define a random variable that represents the time in minutes required to assemble the product.
b. What values may the random variable assume?
c. Is the random variable discrete or continuous?
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3.3 Consider the following data and corresponding weights....
a. Compute the weighted mean.
b. Compute the sample mean of the four data values without weighting. Note the difference in the results provided by the two computations.
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3.4 Consider the following data....What is the mean growth rate over these five periods?
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3.5 Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. Compute the 20th, 25th, 65th, and 75th percentiles.
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3.6 Consider a sample with data values of 53, 55, 70, 58, 64, 57, 53, 69, 57, 68, and 53. Compute the mean, median, and mode.
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3.7 The average number of minutes Americans commute to work is 27.7 minutes (Sterling’s Best Places, April 13, 2012). The average commute time in minutes for 48 cities are as follows:...
a. What is the mean commute time for these 48 cities?
b. Compute the median commute time.
c. Compute the mode.
d. Compute the third quartile.
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3.8 The Wall Street Journal reported that the median salary for middle-level manager jobs was approximately $85,000 (The Wall Street Journal, August 6, 2013). Suppose that an independent study of middle-level managers employed at companies located in Atlanta, Georgia, was conducted to compare the salaries of managers working at firms in Atlanta to the national average. The following data show the salary, in thousands of dollars, for a sample of 15 middle-level managers....
a. Compute the median salary for the sample of 15 middle-level managers. How does the median for this group compare to the median reported by The Wall Street Journal?
b. Compute the mean annual salary and discuss how and why it differs from the median computed in part (a).
c. Compute the first and third quartiles.
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3.9
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3.10 Over a nine-month period, OutdoorGearLab tested hardshell jackets designed for ice climbing, mountaineering, and backpacking. Based on the breathability, durability, versatility, features, mobility, and weight of each jacket, an overall rating ranging from 0 (lowest) to 100 (highest) was assigned to each jacket tested. The following data show the results for 20 top-of-the-line jackets (OutdoorGearLab website, February 27, 2013)....
a. Compute the mean, median, and mode.
b. Compute the first and third quartiles.
c. Compute and interpret the 90th percentile.
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3.11 According to the National Education Association (NEA), teachers generally spend more than 40 hours each week working on instructional duties (NEA website, April 2012). The following data show the number of hours worked per week for a sample of 13 high school science teachers and a sample of 11 high school English teachers....
a. What is the median number of hours worked per week for the sample of 13 high school science teachers?
b. What is the median number of hours worked per week for the sample of 11 high school English teachers?
c. Which group has the highest median number of hours worked per week? What is the difference between the median number of hours worked per week?
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3.12 The Big Bang Theory, a situation comedy featuring Johnny Galecki, Jim Parsons, and Kaley Cuoco, is one of the most watched programs on network television. The first two episodes for the 2011-2012 season premiered on September 22, 2011; the first episode attracted 14.1 million viewers and the second episode attracted 14.7 million viewers. The following table shows the number of viewers in millions for the first 21 episodes of the 2011-2012 season (The Big Bang Theory website, April 17, 2012)....
a. Compute the minimum and maximum number of viewers.
b. Compute the mean, median, and mode.
c. Compute the first and third quartiles.
d. Has viewership grown or declined over the 2011-2012 season? Discuss.
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3.13 In automobile mileage and gasoline-consumption testing, 13 automobiles were road tested for 300 miles in both city and highway driving conditions. The following data were recorded for miles-per-gallon performance....Use the mean, median, and mode to make a statement about the difference in performance for city and highway driving.
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3.14 The data contained in the WEBfile named StateUnemp show the unemployment rate in March 2011 and the unemployment rate in March 2012 for every state and the District of Columbia (Bureau of Labor Statistics website, April 20, 2012). To compare unemployment rates in March 2011 with unemployment rates in March 2012, compute the first quartile, the median, and the third quartile for the March 2011 unemployment data and the March 2012 unemployment data. What do these statistics suggest about the change in unemployment rates across the states?
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3.15 Martinez Auto Supplies has retail stores located in eight cities in California. The price they charge for a particular product in each city varies because of differing competitive conditions. For instance, the price they charge for a case of a popular brand of motor oil in each city follows. Also shown are the number of cases that Martinez Auto sold last quarter in each city....Compute the average sales price per case for this product during the last quarter.
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3.16 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?
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3.17 The following table shows the total return and the number of funds for four categories of mutual funds....
a. Using the number of funds as weights, compute the weighted average total return for these mutual funds.
b. Is there any difficulty associated with using the “number of funds” as the weights in computing the weighted average total return in part (a)? Discuss. What else might be used for weights?
c. Suppose you invested $10,000 in this group of mutual funds and diversified the investment by placing $2000 in Domestic Equity funds, $4000 in International Equity funds, $3000 in Specialty Stock funds, and $1000 in Hybrid funds. What is the expected return on the portfolio?
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3.18 Based on a survey of 425 master’s programs in business administration, U.S. News & World Report ranked the Indiana University Kelley Business School as the 20th best business program in the country (America’s Best Graduate Schools, 2009). The ranking was based in part on surveys of business school deans and corporate recruiters. Each survey respondent was asked to rate the overall academic quality of the master’s program on a scale from 1 “marginal” to 5 “outstanding.” Use the sample of responses shown in the following table to compute the weighted mean score for the business school deans and the corporate recruiters. Discuss....
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3.19
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3.20
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3.21 If an asset declines in value from $5000 to $3500 over nine years, what is the mean annual growth rate in the asset’s value over these nine years?
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3.22 The current value of a company is $25 million. If the value of the company six years ago was $10 million, what is the company’s mean annual growth rate over the past six years?
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3.23 Consider a sample with data values of 10, 20, 12, 17, and 16. Compute the range and interquartile range.
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3.24 Consider a sample with data values of 10, 20, 12, 17, and 16. Compute the variance and standard deviation.
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3.25 Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. Compute the range, interquartile range, variance, and standard deviation.
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3.26 Data collected by the Oil Price Information Service from more than 90,000 gasoline and convenience stores throughout the U.S. showed that the average price for a gallon of unleaded gasoline was $3.28 (MSN Auto website, February 2, 2014). The following data show the price per gallon ($) for a sample of 20 gasoline and convenience stores located in San Francisco....
a. Use the sample data to estimate the mean price for a gallon of unleaded gasoline in San Francisco.
b. Compute the sample standard deviation.
c. Compare the mean price per gallon for the sample data to the national average price. What conclusions can you draw about the cost living in San Francisco?
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3.27 The results of a search to find the least expensive round-trip flights to Atlanta and Salt Lake City from 14 major U.S. cities are shown in the following table. The departure date was June 20, 2012, and the return date was June 27, 2012....
a. Compute the mean price for a round-trip flight into Atlanta and the mean price for a round-trip flight into Salt Lake City. Is Atlanta less expensive to fly into than Salt Lake City? If so, what could explain this difference?
b. Compute the range, variance, and standard deviation for the two samples. What does this information tell you about the prices for flights into these two cities?
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3.28 The Australian Open is the first of the four Grand Slam professional tennis events held each year. Victoria Azarenka beat Maria Sharapova to win the 2012 Australian Open women’s title (Washington Post, January 27, 2012). During the tournament Ms. Azarenka’s serve speed reached 178 kilometers per hour. A list of the 20 Women’s Singles serve speed leaders for the 2012 Australian Open is provided in the following table....
a. Compute the mean, variance, and standard deviation for the serve speeds.
b. A similar sample of the 20 Women’s Singles serve speed leaders for the 2011 Wimbledon tournament showed a sample mean serve speed of 182.5 kilometers per hour. The variance and standard deviation were 33.3 and 5.77, respectively. Discuss any difference between the serve speeds in the Australian Open and the Wimbledon women’s tournaments.
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3.29 The LosAngeles Times regularly reports the air quality index for various areas of Southern California. A sample of air quality index values for Pomona provided the following data: 28, 42, 58, 48, 45, 55, 60, 49, and 50.
a. Compute the range and interquartile range.
b. Compute the sample variance and sample standard deviation.
c. A sample of air quality index readings for Anaheim provided a sample mean of 48.5, a sample variance of 136, and a sample standard deviation of 11.66. What comparisons can you make between the air quality in Pomona and that in Anaheim on the basis of these descriptive statistics?
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3.30 The following data were used to construct the histograms of the number of days required to fill orders for Dawson Supply, Inc., and J.C. Clark Distributors (see Figure 3.5)....Use the range and standard deviation to support the previous observation that Dawson Supply provides the more consistent and reliable delivery times.
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3.31 The results of Accounting Principals’ latest Workonomix survey indicate the average American worker spends $1092 on coffee annually (The Consumerist, January 20, 2012). To determine if there are any differences in coffee expenditures by age group, samples of 10 consumers were selected for three age groups (18-34, 35-44, and 45 and Older). The dollar amount each consumer in the sample spent last year on coffee is provided below....
a. Compute the mean, variance, and standard deviation for each of these three samples.
b. What observations can be made based on these data?
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3.32 Advertising Age annually compiles a list of the 100 companies that spend the most on advertising. Consumer-goods company Procter & Gamble has often topped the list, spending billions of dollars annually (Advertising Age website, March 12, 2013). Consider the data found in the file Advertising. It contains annual advertising expenditures for a sample of 20 companies in the automotive sector and 20 companies in the department store sector.
a. What is the mean advertising spent for each sector?
b. What is the standard deviation for each sector?
c. What is the range of advertising spent for each sector?
d. What is the interquartile range for each sector?
e. Based on this sample and your answers to parts (a) to (d), comment on any differences in the advertising spending in the automotive companies versus the department store companies.
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3.33
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3.34 The following times were recorded by the quarter-mile and mile runners of a university track team (times are in minutes)....After viewing this sample of running times, one of the coaches commented that the quarter-milers turned in the more consistent times. Use the standard deviation and the coefficient of variation to summarize the variability in the data. Does the use of the coefficient of variation indicate that the coach’s statement should be qualified?
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3.35 Consider a sample with data values of 10, 20, 12, 17, and 16. Compute the z-score for each of the five observations.
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3.36 Consider a sample with a mean of 500 and a standard deviation of 100. What are the z-scores for the following data values: 520, 650, 500, 450, and 280?
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3.37 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
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3.38 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
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3.39 The results of a national survey showed that on average, adults sleep 6.9 hours per night. Suppose that the standard deviation is 1.2 hours.
a. Use Chebyshev’s theorem to calculate the percentage of individuals who sleep between 4.5 and 9.3 hours.
b. Use Chebyshev’s theorem to calculate the percentage of individuals who sleep between 3.9 and 9.9 hours.
c. Assume that the number of hours of sleep follows a bell-shaped distribution. Use the empirical rule to calculate the percentage of individuals who sleep between 4.5 and 9.3 hours per day. How does this result compare to the value that you obtained using Chebyshev’s theorem in part (a)?
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3.40 The Energy Information Administration reported that the mean retail price per gallon of regular grade gasoline was $3.43 (Energy Information Administration, July 2012). Suppose that the standard deviation was $.10 and that the retail price per gallon has a bellshaped distribution.
a. What percentage of regular grade gasoline sold between $3.33 and $3.53 per gallon?
b. What percentage of regular grade gasoline sold between $3.33 and $3.63 per gallon?
c. What percentage of regular grade gasoline sold for more than $3.63 per gallon?
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3.41
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3.42 Many families in California are using backyard structures for home offices, art studios, and hobby areas as well as for additional storage. Suppose that the mean price for a customized wooden, shingled backyard structure is $3100. 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. If the cost for a backyard shed-office combination built in Albany, California, is $13,000, should this structure be considered an outlier? Explain.
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3.43 According to a Los Angeles Times study of more than 1 million medical dispatches from 2007 to 2012, the 911 response time for medical aid varies dramatically across Los Angeles (LA Times website, November 2012). Under national standards adopted by the Los Angeles Fire Department, rescuers are supposed to arrive within six minutes to almost all medical emergencies. But the Times analysis found that in affluent hillside communities stretching from Griffith Park to Pacific Palisades, firefighters failed to hit that mark nearly 85% of the time.The following data show the response times, in minutes, for 10 emergency calls in the Griffith Park neighborhood....Based on this sample of ten response times, compute the descriptive statistics in parts (a) and (b) and then answer the questions in parts (c) and (d):
a. Mean, median, and mode
b. Range and standard deviation
c. Should the response time of 8.3 minutes be considered an outlier in comparison to the other response times?
d. Do the response times indicate that the city is meeting the national standards? Should the city consider making changes to its response strategies? Would adding more stations to areas in the city be a practical solution? Discuss.
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3.44 A sample of 10 NCAA college basketball game scores provided the following data....
a. Compute the mean and standard deviation for the points scored by the winning team.
b. Assume that the points scored by the winning teams for all NCAA games follow a bell-shaped distribution. Using the mean and standard deviation found in part (a), estimate the percentage of all NCAA games in which the winning team scores 84 or more points. Estimate the percentage of NCAA games in which the winning team scores more than 90 points.
c. Compute the mean and standard deviation for the winning margin. Do the data contain outliers? Explain.
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3.45 The Wall Street Journal reported that Walmart Stores Inc. is planning to lay off 2300 employees at its Sam’s Club warehouse unit. Approximately half of the layoffs will be hourly employees (The Wall Street Journal, January 25-26, 2014). Suppose the following data represent the percentage of hourly employees laid off for 15 Sam’s Club stores....
a. Compute the mean and median percentage of hourly employees being laid off at these stores.
b. Compute the first and third quartiles.
c. Compute the range and interquartile range.
d. Compute the variance and standard deviation.
e. Do the data contain any outliers?
f. Based on the sample data, does it appear that Walmart is meeting its goal for reducing the number of hourly employees?
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3.46 Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. Provide the five-number summary for the data.
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3.47 Show the box plot for the data in exercise 46.
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3.48 Show the five-number summary and the box plot for the following data: 5, 15, 18, 10, 8, 12, 16, 10, 6.
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3.49 A data set has a first quartile of 42 and a third quartile of 50. Compute the lower and upper limits for the corresponding box plot. Should a data value of 65 be considered an outlier?
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3.50 Naples, Florida, hosts a half-marathon (13.1-mile race) in January each year. The event attracts top runners from throughout the United States as well as from around the world. In January 2009, 22 men and 31 women entered the 19-24 age class. Finish times in minutes are as follows (Naples Daily News, January 19, 2009). Times are shown in order of finish....
a. George Towett of Marietta, Georgia, finished in first place for the men and Lauren Wald of Gainesville, Florida, finished in first place for the women. Compare the first-place finish times for men and women. If the 53 men and women runners had competed as one group, in what place would Lauren have finished?
b. What is the median time for men and women runners? Compare men and women runners based on their median times.
c. Provide a five-number summary for both the men and the women.
d. Are there outliers in either group?
e. Show the box plots for the two groups. Did men or women have the most variation in finish times? Explain.
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3.51 Annual sales, in millions of dollars, for 21 pharmaceutical companies follow....
a. Provide a five-number summary.
b. Compute the lower and upper limits.
c. Do the data contain any outliers?
d. Johnson & Johnson’s sales are the largest on the list at $14,138 million. Suppose a data entry error (a transposition) had been made and the sales had been entered as $41,138 million. Would the method of detecting outliers in part (c) identify this problem and allow for correction of the data entry error?
e. Show a box plot.
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3.52 Consumer Reports provided overall customer satisfaction scores for AT&T, Sprint, T-Mobile, and Verizon cell-phone services in major metropolitan areas throughout the United States. The rating for each service reflects the overall customer satisfaction considering a variety of factors such as cost, connectivity problems, dropped calls, static interference, and customer support. A satisfaction scale from 0 to 100 was used with 0 indicating completely dissatisfied and 100 indicating completely satisfied. The ratings for the four cell-phone services in 20 metropolitan areas are as shown (Consumer Reports, January 2009)....
a. Consider T-Mobile first. What is the median rating?
b. Develop a five-number summary for the T-Mobile service.
c. Are there outliers for T-Mobile? Explain.
d. Repeat parts (b) and (c) for the other three cell-phone services.
e. Show the box plots for the four cell-phone services on one graph. Discuss what a comparison of the box plots tells about the four services. Which service did Consumer Reports recommend as being best in terms of overall customer satisfaction?
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3.53 Fortune magazine's list of the world most admired companies for 2014 is provided the data contained in the WEBfile named AdmiredCompanies (Fortune, March 17, 2014). The data in the column labelled Return shows the one-year total return (%) for the top ranked 50 companies. For the same time period the S&P average return was 18.4%.
a. Compute the median return for the top ranked 50 companies.
b. What percentage of the top-ranked 50 companies had a one-year return greater than the S&P average return?
c. Develop the five-number summary for the data.
d. Are there any outliers?
e. Develop a box plot for the one-year total return.
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3.54 The Bureau of Transportation Statistics keeps track of all border crossings through ports of entry along the U.S.-Canadian and U.S.-Mexican borders. The data contained in the WEBfile named BorderCrossings show the most recently published figures for the number of personal vehicle crossings (rounded to the nearest 1000) at the 50 busiest ports of entry during the month of August (U.S. Department of Transportation website, February 28, 2013).
a. What are the mean and median number of crossings for these ports of entry?
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.
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3.55 Five observations taken for two variables follow....
a. Develop a scatter diagram with x on the horizontal axis.
b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?
c. Compute and interpret the sample covariance.
d. Compute and interpret the sample correlation coefficient.
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3.56 Five observations taken for two variables follow....
a. Develop a scatter diagram for these data.
b. What does the scatter diagram indicate about a relationship between x and y?
c. Compute and interpret the sample covariance.
d. Compute and interpret the sample correlation coefficient.
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3.57
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3.58 A department of transportation’s study on driving speed and miles per gallon for midsize automobiles resulted in the following data:...Compute and interpret the sample correlation coefficient.
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3.59
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3.60 The Russell 1000 is a stock market index consisting of the largest U.S. companies. The Dow Jones Industrial Average is based on 30 large companies. The file Russell gives the annual percentage returns for each of these stock indexes for the years 1988 to 2012 (1stock1 website).
a. Plot these percentage returns using a scatter plot.
b. Compute the sample mean and standard deviation for each index.
c. Compute the sample correlation.
d. Discuss similarities and differences in these two indexes.
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3.61 A random sample of 30 colleges from Kiplinger’s list of the best values in private college provided the data shown in the WEBfile named BestPrivateColleges (Kiplinger, October 2013). The variable named Admit Rate (%) shows the percentage of students that applied to the college and were admitted, and the variable named 4-yr Grad. Rate (%) shows the percentage of students that were admitted and graduated in four years.
a. Develop a scatter diagram with Admit Rate (%) as the independent variable. What does the scatter diagram indicate about the relationship between the two variables?
b. Compute the sample correlation coefficient. What does the value of the sample correlation coefficient indicate about the relationship between the Admit Rate (%) and the 4-yr Grad. Rate (%)?
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3.62 The average number of times Americans dine out in a week fell from 4.0 in 2008 to 3.8 in 2012 (Zagat.com, April 1, 2012). The number of times a sample of 20 families dined out last week 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 0.34. Comment on the shape of this distribution. Is it the shape you would expect? Why or why not?
f. Do the data contain outliers?
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3.63 USA Today reports that NCAA colleges and universities are paying higher salaries to a newly recruited football coach compared to what they paid their previous football coach. (USA Today, February 12, 2013). The annual base salaries for the previous head football coach and the new head football coach at 23 schools are given in the file Coaches.
a. Determine the median annual salary for a previous head football coach and a new head football coach.
b. Compute the range for salaries for both previous and new head football coaches.
c. Compute the standard deviation for salaries for both previous and new head football coaches.
d. Based on your answers to (a) to (c), comment on any differences between the annual base salary a school pays a new head football coach compared to what it paid its pervious head football coach.
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3.64 The average waiting time for a patient at an El Paso physician’s office is just over 29 minutes, well above the national average of 21 minutes. In fact, El Paso has the longest physician’s office waiting times in the United States (El Paso Times, January 8, 2012). In order to address the issue of long patient wait times, some physicians’ offices are using wait tracking systems to notify patients of expected wait times. Patients can adjust their arrival times based on this information and spend less time in waiting rooms. The following data show wait times (minutes) for a sample of patients at offices that do not have an office tracking system and wait times for a sample of patients at offices with an office tracking system....
a. What are the mean and median patient wait times for offices with a wait tracking system? What are the mean and median patient wait times for offices without a wait tracking system?
b. What are the variance and standard deviation of patient wait times for offices with a wait tracking system? What are the variance and standard deviation of patient wait times for visits to offices without a wait tracking system?
c. Do offices with a wait tracking system have shorter patient wait times than offices without a wait tracking system? Explain.
d. Considering only offices without a wait tracking system, what is the z-score for the tenth patient in the sample?
e. Considering only offices with a wait tracking system, what is the z-score for the sixth patient in the sample? How does this z-score compare with the z-score you calculated for part (d)?
f. Based on z-scores, do the data for offices without a wait tracking system contain any outliers? Based on z-scores, do the data for offices with a wait tracking system contain any outliers?
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3.65 U.S. companies lose $63.2 billion per year from workers with insomnia. Workers lose an average of 7.8 days of productivity per year due to lack of sleep (Wall Street Journal, January 23, 2013). The following data show the number of hours of sleep attained during a recent night for a sample of 20 workers....
a. What is the mean number of hours of sleep for this sample?
b. What is the variance? Standard deviation?
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3.66 A study of smartphone users shows that 68% of smartphone use occurs at home and a user spends an average of 410 minutes per month using a smartphone to interact with other people (Harvard Business Review, January-February 2013). Consider the following data indicating the number of minutes in a month spent interacting with others via a smartphone for a sample of 50 smartphone users....
a. What is the mean number of minutes spent interacting with others for this sample? How does it compare to the mean reported in the study?
b. What is the standard deviation for this sample?
c. Are there any outliers in this sample?
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3.67 Public transportation and the automobile are two methods an employee can use to get to work each day. Samples of times recorded for each method are shown. Times are in minutes....
a. Compute the sample mean time to get to work for each method.
b. Compute the sample standard deviation for each method.
c. On the basis of your results from parts (a) and (b), which method of transportation should be preferred? Explain.
d. Develop a box plot for each method. Does a comparison of the box plots support your conclusion in part (c)?
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3.68 In 2007 the New York Times reported that the median annual household income in the United States was $55,500 (New York Times website, August, 21, 2013). Answer the following questions based on the following sample of 14 household incomes for 2013 ($1000s)....
a. What is the median household income for the sample data for 2013?
b. Based on the sample data, estimate the percentage change in the median household income from 2007 to 2013.
c. Compute the first and third quartiles.
d. Provide a five-number summary.
e. Using the z-score approach, do the data contain any outliers? Does the approach that uses the values of the first and third quartiles and the interquartile range to detect outliers provide the same results?
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3.69 The data contained in the WEBfile named FoodIndustry show the company/chain name, the average sales per store ($ 1000s), and the food segment industry for 47 restaurant chains (Quick Service Restaurant Magazine website, August 2013).
a. What was the mean U.S. sales per store for the 47 restaurant chains?
b. What are the first and third quartiles? What is your interpretation of the quartiles?
c. Show a box plot for the level of sales and discuss if there are any outliers in terms of sales that would skew the results.
d. Develop a frequency distribution showing the average sales per store for each segment. Comment on the results obtained.
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3.70 Travel + Leisure magazine presented its annual list of the 500 best hotels in the world (Travel + Leisure, January 2009). The magazine provides a rating for each hotel along with a brief description that includes the size of the hotel, amenities, and the cost per night for a double room. A sample of 12 of the top-rated hotels in the United States follows....
a. What is the mean number of rooms?
b. What is the mean cost per night for a double room?
c. Develop a scatter diagram with the number of rooms on the horizontal axis and the cost per night on the vertical axis. Does there appear to be a relationship between the number of rooms and the cost per night? Discuss.
d. What is the sample correlation coefficient? What does it tell you about the relationship between the number of rooms and the cost per night for a double room? Does this appear reasonable? Discuss.
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3.71 The 32 teams in the National Football League (NFL) are worth, on average, $1.17 billion, 5% more than last year. The following data show the annual revenue ($ millions) and the estimated team value ($ millions) for the 32 NFL teams (Forbes website, February 28, 2014)....
a. Develop a scatter diagram with Revenue on the horizontal axis and Value on the vertical axis. Does there appear that there are any relationship between the two variables?
b. What is the sample correlation coefficient? What can you say about the strength of the relationship between Revenue and Value?
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3.72 Does a major league baseball team’s record during spring training indicate how the team will play during the regular season? Over the last six years, the correlation coefficient between a team’s winning percentage in spring training and its winning percentage in the regular season is .18 (The Wall Street Journal, March 30, 2009)....Shown are the winning percentages for the 14 American League teams during the 2008 season.
a. What is the correlation coefficient between the spring training and the regular season winning percentages?
b. What is your conclusion about a team’s record during spring training indicating how the team will play during the regular season? What are some of the reasons why this occurs? Discuss.
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3.73 The days to maturity for a sample of five money market funds are shown here. The dollar amounts invested in the funds are provided. Use the weighted mean to determine the mean number of days to maturity for dollars invested in these five money market funds....
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3.74 Automobiles traveling on a road with a posted speed limit of 55 miles per hour are checked for speed by a state police radar system. Following is a frequency distribution of speeds....
a. What is the mean speed of the automobiles traveling on this road?
b. Compute the variance and the standard deviation.
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3.75 The Panama Railroad Company was established in 1850 to construct a railroad across the isthmus that would allow fast and easy access between the Atlantic and Pacific Oceans. The following table provides annual returns for Panama Railroad stock from 1853 through 1880 (The Big Ditch, Mauer and Yu, 2011).
a. Create a graph of the annual returns on the stock. The New York Stock Exchange earned an annual average return of 8.4% from 1853 through 1880. Can you tell from the graph if the Panama Railroad Company stock outperformed the New York Stock Exchange?
b. Calculate the mean annual return on Panama Railroad Company stock from 1853 through 1880. Did the stock outperform the New York Stock Exchange over the same period?
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