Essentials of Modern Business Statistics

David R. Anderson, Dennis J. Sweeney,Thomas A. Williams

Chapter 3

Descriptive Statistics: Numerical Measures - all with Video Answers

Educators

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Chapter Questions

Problem 1

Consider a sample with data values of $10,20,12,17,$ and $16 .$ Compute the mean and median.

AY

Aria Ye

Numerade Educator

Problem 2

Consider a sample with data values of $10,20,21,17,16,$ and $12 .$ Compute the mean and
median.

Megha Nayar

Numerade Educator

Problem 4

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.

Megha Nayar

Numerade Educator

Problem 5

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 quartie?

Bryan Luo

Numerade Educator

Problem 6

During the $2007-2008 \mathrm{NCA}$ A 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 NCA basketball games during the $2008-2009$ season.
a. What is the mean number of 3-point shots taken per game?
b. What is the mean number of 3-point shots made per game?
c. Using the closer 3 -point line, players were making 35.2$\%$ of their shots. What percentage of shots were players making from the new 3 -point line?
d. What was the impact of the NCAA rules change that moved the 3 -point line back to
20 feet, 9 inches for the $2008-2009$ season? Would you agree with the Associated
Press Sports article that stated, "Moving back the 3 -point line hasn't changed the game
dramatically"? Explain.

Srikar Katta

Numerade Educator

Problem 7

Endowment income is a critical part of the annual budgets at colleges and universities.
A study by the National Association of College and University Business Officers reported that the 435 colleges and universities surveyed held a total of $\$ 413$ billion in
endowments. The 10 wealthiest universities are shown below (The Wall Street Journal,
January $27,2009$ ). Amounts are in billions of dollars.
a. What is the mean endowment for these universities?
b. What is the median endowment?
c. What is the mode endowment?
d. Compute the first and third quartiles.
e. What is the total endowment at these 10 universities? These universities represent
2.3$\%$ of the 435 colleges and universities surveyed. What percentage of the total $\$ 413$
billion in endowments is held by these 10 universities?
f. The Wall Street Journal reported that over a recent five-month period, a downturn
in the economy has caused endowments to decline 23$\% .$ What is the estimate of the
dollar amount of the decline in the total endowments held by these 10 universities? Given this situation, what are some of the steps you would expect university administrators to be considering?

Bryan Luo

Numerade Educator

Problem 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.
$\begin{array}{ccccc}{120} & {230} & {110} & {115} & {160} \\ {130} & {150} & {105} & {195} & {155} \\ {105} & {360} & {120} & {120} & {140} \\ {100} & {115} & {180} & {235} & {255}\end{array}$
a. Compute the mean, median, and mode.
b. Compute the first and third quartiles.
c. Compute and interpret the 90th percentile.

Srikar Katta

Numerade Educator

Problem 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:
$$\begin{array}{llllllll}{\text {Existing Homes}} & {315.5} & {202.5} & {140.2} & {181.3} & {470.2} & {169.9} & {112.8} & {230.0} & {177.5} \\ {\text {New Homes}} & {275.9} & {350.2} & {195.8} & {525.0} & {225.3} & {215.5} & {175.0} & {149.5}\end{array}$$
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?

Bryan Luo

Numerade Educator

Problem 10

A panel of economists provided forecasts of the U.S. economy for the first six months of
2007 (The Wall Street Journal, January $2,2007 ) .$ The percent changes in the gross domes-
tic product (GDP) forecasted by 30 economists are as follows.
$\begin{array}{ccccccccc}{2.6} & {3.1} & {2.3} & {2.7} & {3.4} & {0.4} & {0.9} & {2.6} & {2.8} & {2.0} & {2.4} \\ {2.7} & {2.7} & {2.7} & {2.9} & {3.1} & {2.8} & {1.7} & {2.3} & {2.8} & {3.5} \\ {0.4} & {2.5} & {2.2} & {1.9} & {1.8} & {1.1} & {2.0} & {2.1} & {2.5} & {0.5}\end{array}$
a. What is the minimum forecast for the percent change in the GDP? What is the
maximum?
b. Compute the mean, median, and mode.
c. Compute the first and third quartiles.
d. Did the economists provide an optimistic or pessimistic outlook for the U.S. economy?
Discuss.

Srikar Katta

Numerade Educator

Problem 11

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.
$\begin{array}{lllllllllll}{\text { City: }} & {16.2} & {16.7} & {15.9} & {14.4} & {13.2} & {15.3} & {16.8} & {16.0} & {16.1} & {15.3} & {15.2} & {15.3} & {16.2} \\ {\text {Highway: }} & {19.4} & {20.6} & {18.3} & {18.6} & {19.2} & {17.4} & {17.2} & {18.6} & {19.0} & {21.1} & {19.4} & {18.5} & {18.7}\end{array}$
Use the mean, median, and mode to make a statement about the difference in performance for city and highway driving.

NP

Niki Petrakos

Numerade Educator

Problem 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.

Zach Steedman

Numerade Educator

Problem 13

Consider a sample with data values of $10,20,12,17,$ and $16 .$ Compute the range and interquartile range.

N E

Numerade Educator

Problem 14

Consider a sample with data values of $10,20,12,17,$ and $16 .$ Compute the variance and
standard deviation.

Zach Steedman

Numerade Educator

Problem 15

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.

Paul A.

California State Polytechnic University, Pomona

Problem 16

A bowler's scores for six games were $182,168,188,190,170,170,$ and $174 .$ Using these data
as a sample, compute the following descriptive statistics:
a. Range
b. Variance
c. Standard deviation
d. Coefficient of variation

Zach Steedman

Numerade Educator

Problem 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?

Nick Johnson

Numerade Educator

Problem 18

Car rental rates per day for a sampleof seven Eastern U.S. cities are as follows (The Wall Street
Journal, January $16,2004 ) .$
$$\begin{array}{ll}{\text { City }} & {\text { Daily Rate }} \\ {\text { Boston }} & {\$ 43} \\ {\text { Atlanta }} & {\$ 5} \\ {\text { Miami }} & {34} \\ {\text { New York }} & {58} \\ {\text { Orlando }} & {30} \\ {\text { Pittsburgh }} & {30} \\ {\text { Washington, D.C. }} & {36}\end{array}$$
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 S38 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.

Zach Steedman

Numerade Educator

Problem 19

The Los Angeles Times regularly reports the air quality index for various areas of South-
ern 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 compari-
sons can you make between the air quality in Pomona and that in Anaheim on the basis
of these descriptive statistics?

Nick Johnson

Numerade Educator

Problem 20

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 3.4).
Dawson Supply Days for Delivery: 11$\quad 10 \quad 9 \quad 10 \quad 11 \quad 11 \quad 10 \quad 11 \quad 10 \quad 10$
Clark Distributors Days for Delivery: 8$\quad 10 \quad 13 \quad 7 \quad 10 \quad 11 \quad 10 \quad 7 \quad 15 \quad 12$
Use the range and standard deviation to support the previous observation that Dawson
Supply provides the more consistent and reliable delivery times.

Zach Steedman

Numerade Educator

Problem 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, 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?

Tim Schmuhl

Numerade Educator

Problem 22

The National Retail Federation reported that college freshmen spend more on back-to- school items than any other college group $(U S A$ Today, August $4,2006) .$ Sample data comparing the back-to-school expenditures for 25 freshmen and 20 seniors are shown in the data file Back To School.
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?

Paul A.

California State Polytechnic University, Pomona

Problem 23

Scores turned in by an amateur golfer at the Bonita Fairways Golf Course in Bonita Springs, Florida, during 2005 and 2006 are as follows:
$$\begin{array}{llllllll}{2005 \text { Season: }} & {74} & {78} & {79} & {77} & {75} & {73} & {75} & {77} \\ {2006 \text { Season:}} & {71} & {70} & {75} & {77} & {85} & {80} & {71} & {79}\end{array}$$
a. Use the mean and standard deviation to evaluate the golfer's performance over the two-year period.
b. What is the primary difference in performance between 2005 and 2006$?$ What improvement, if any, can be seen in the 2006 scores?

Norman Atentar

Numerade Educator

Problem 24

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?

Zach Steedman

Numerade Educator

Problem 25

Consider a sample with data values of $10,20,12,17,$ and $16 .$ Compute the $z$ -score for each
of the five observations.

Bryan Luo

Numerade Educator

Problem 26

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$?$

Zach Steedman

Numerade Educator

Problem 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:
$$\begin{array}{ll}{\text { a. }} & {20 \text { to } 40} \\ {\text { b. }} & {15 \text { to } 45} \\ {\text { c. }} & {22 \text { to } 38} \\ {\text { d. }} & {18 \text { to } 42} \\ {\text { e. }} & {12 \text { to } 48}\end{array}$$

Harsh Gadhiya

Numerade Educator

Problem 28

Suppose the data have a bell-shaped distribution with a mean of 30 and a standard devia-
tion of $5 .$ Use the empirical rule to determine the percentage of data within each of the
following ranges:
$\begin{array}{ll}{\text { a. }} & {20 \text { to } 40} \\ {\text { b. }} & {15 \text { to } 45} \\ {\text { c. }} & {25 \text { to } 35}\end{array}$

Zach Steedman

Numerade Educator

Problem 29

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)?

Kari Hasz

Numerade Educator

Problem 30

The Energy Information Administration reported that the mean retail price per gallon of
regular grade gasoline was $\$ 2.81$ (Energy Information Administration, November $2010 ) .$
Suppose that the standard deviation was $S .10$ and that the retail price per gallon has a bell-
shaped distribution.
a. What percentage of regular grade gasoline sold between $\$ 2.71$ and $\$ 2.91$ per gallon?
b. What percentage of regular grade gasoline sold between $\$ 2.71$ and $\$ 3.01$ per gallon?
c. What percentage of regular grade gasoline sold for more than $\$ 3.01$ per gallon?

Zach Steedman

Numerade Educator

Problem 31

The national average for the math portion of the College Board's SAT is 515 (The World
Almanac, 2009 ). The College Board periodically rescales the test scores such that the
standard deviation is approximately $100 .$ Answer the following questions using a bell-
shaped distribution and the empirical rule for the verbal test scores.
a. What percentage of students have an SAT math score greater than 615$?$
b. What percentage of students have an SAT math score greater than 715$?$
c. What percentage of students have an SAT math score between 415 and 515$?$
d. What percentage of students have an SAT math score between 315 and 615$?$

DC

Dominic Chaulk

Numerade Educator

Problem 32

Many families in California are using backyardstructures 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, Califomia, is
$\$ 13,000,$ should this structure be considered an outlier? Explain.

Zach Steedman

Numerade Educator

Problem 33

Recently, management at Oak Tree Golf Course received a few complaints about the condition of the greens. Several players complained that the greens are too fast. Rather than react to the comments of just a few, the Golf Association conducted a survey of 100 male and 100 female golfers. The survey results are summarized here.
a. Combine these two crosstabulations into one, with Male and Female as the row labels and Too Fast and Fine as the column labels. Which group shows the highest percentage saying that the greens are too fast?
b. Refer to the initial crosstabulations. For those players with low handicaps (better players), which group (male or female) shows the highest percentage saying the greens are too fast?
c. Refer to the initial crosstabulations. For those players with higher handicaps, which group (male or female) shows the highest percentage saying the greens are too fast?
d. What conclusions can you draw about the preferences of men and women concerning the speed of the greens? Are the conclusions you draw from part (a) as compared with parts (b) and (c) consistent? Explain any apparent inconsistencies.

Dominador Tan

Numerade Educator

Problem 34

A sample of 10 $\mathrm{NCA}$ A college basketball game scores provided the following data $(U S A$ Today, January $26,2004 ) .$
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.
compute the mean and standard deviation for the winning margin. Do the data con-
tain outliers? Explain.

Zach Steedman

Numerade Educator

Problem 35

The Associated Press Team Marketing Report listed the Dallas Cowboys as the team with the highest ticket prices in the National Football League (USA Today, October $\$20,2009 )$. Data showing the average ticket price for a sample of 14 teams in the National Football League are as follows.
a. What is the mean ticket price?
b. The previous year, the mean ticket price was $\$ 72.20 .$ What was the percentage increase
in the mean ticket price for the one-year period?
c. Compute the median ticket price.
d. Compute the first and third quartiles.
e. Compute the standard deviation.
f. What is the $z$ -score for the Dallas Cowboys ticket price? Should this price be considered an outlier? Explain.

Evelyn Cunningham

Evelyn Cunningham

Numerade Educator

Problem 36

Consider a sample with data values of $27,25,20,15,30,34,28,$ and $25 .$ Provide the five-
number summary for the data.

Zach Steedman

Numerade Educator

Problem 37

Show the box plot for the data in exercise $36 .$

Nick Johnson

Numerade Educator

Problem 38

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

Zach Steedman

Numerade Educator

Problem 39

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?

Nick Johnson

Numerade Educator

Problem 40

Some of the most well-known food franchises and the number of retail locations for each
are shown below (The New York Times Almanac, 2010 ).
a. What is the largest franchise? How many retail locations does it have?
b. What is the median number of locations for the franchises?
c. Provide a five-number summary.
d. Are there any outtiers?
e. Show the box plot.

Zach Steedman

Numerade Educator

Problem 41

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 Lave 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.

Jason Gerber

Numerade Educator

Problem 42

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 propped 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 did Consumer
Reports recommend as being best in terms of overall customer satisfaction?

Zach Steedman

Numerade Educator

Problem 43

The Philadelphia Phillies defeated the Tampa Bay Rays in the fifth game by a score of 4 to
3 to win the 2008 major league baseball World Series (The Philadelphia Inquirer, October
$29,2008$ ). Earlier in the major league baseball playoffs, the Philadelphia Phillies defeated the Los Angeles Dodgers to win the National League Championship, while the Tampa Bay
Rays defeated the Boston Red Sox to win the American League Championship. The file
MLBSalaries contains the salaries for the 28 players on each of these four teams (USA
Today Salary Database, October 2008 ). The data, shown in thousands of dollars, have been
ordered from the highest salary to the lowest salary for each team.
a. Analyze the salaries for the World Champion Philadelphia Phillies. What is the total payroll for the team? What is the median salary? What is the five-number
summary?
b. Were there salary outliers for the Philadelphia Phillies? If so, how many and what were
the salary amounts?
c. $\quad$ What is the total payroll for each of the other three teams? Develop the five-number
summary for each team and identify any outliers.
d. Show the box plots of the salaries for all four teams. What are your intemretations?
Of these four teams, does it appear that the team with the higher salaries won the
league championships and the World Series?

Paul A.

California State Polytechnic University, Pomona

Problem 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 quartics?
c. Provide a five-number summary.
d. Do the data contain any outliers? Show a box plot.

Zach Steedman

Numerade Educator

Problem 45

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.

Harsh Gadhiya

Numerade Educator

Problem 46

Five observations taken for two variables follow.
a. Developa 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.

Zach Steedman

Numerade Educator

Problem 47

Ten major college football bowl games were played in January $2010,$ with the University
of Alabama beating the University of Texas 37 to 21 to become the national champion
of college football. The results of the ten bowl games are shown below $(U S A$ Today, January $8,2010$ ). The predicted winning point margin was based on Las Vegas betting
odds approximately one week before the bowl games were played. For example, Auburn
was predicted to beat Northwestern in the Outback Bowl by five points. The actual winning point margin for Auburn was three points. A negative predicted winning point
margin means that the team that won the bowl game was an underdog and expected to
lose. For example, in the Rose Bowl, Ohio State was a two-point underdog to Oregon and
ended up winning by nine points.
a. Develop a scatter diagram with predicted point margin on the horizontal axis.
b. What is the relationship between predicted and actual point margins?
c. Compute and interpret the sample covariance.
d. Compute the sample correlation coefficient. What does this value indicate about the
relationship between the Las Vegas predicted point margin and the actual point mar-
gin in college football bowl games?

Ryan Gardner

Numerade Educator

Problem 48

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.

Zach Steedman

Numerade Educator

Problem 49

At the beginning of $2009,$ the economic downturn resulted in the loss of jobs and an
increase in delinquent loans for housing. The national unemployment rate was 6.5$\%$ and
the percentage of delinquent loans was 6.12$\%$ (The Wall Street Journal, January $27,2009$ ). In projecting where the real estate market was headed in the coming year, economists
studied the relationship between the jobless rate and the percentage of delinquent loans.
The expectation was that if the jobless rate continued to increase, there would also be an increase in the percentage of delinquent loans. The data below show the jobless rate and
the delinquent loan percentage for 27 major real estate markets.
a. Compute the correlation coefficient. Is there a positive correlation between the jobless
rate and the percentage of delinquent housing loans? What is your interpretation?
b. Show a scatter diagram of the relationship between jobless rate and the percentage of
delinquent housing loans.

Tim Schmuhl

Numerade Educator

Problem 50

The Dow Jones Industrial Average (DJIA) and the Standard \& Poor's 500 Index (S\&P 500$)$ .
are both used to measure the performance of the stock market. The DJIA is based on the price of stocks for 30 large companies; the S\&P 500 is based on the price of stocks for 5000
companies. If both the DJIA and S\&P 500 measure the performance of the stock market, how are they correlated? The following data show the daily percent increase or daily
percent decrease in the DJIA and S\&P 500 for a sample of nine days over a three-month period (The Wall Street Journal, January 15 to March $10,2006 )$
a. Show a scatter diagram.
b. Compute the sample correlation coefficient for these data.
c. Discuss the association between the DJIA and S\&P 500. Do you need to check both
before having a general idea about the daily stock market performance?

Zach Steedman

Numerade Educator

Problem 51

The daily high andlow temperatures for 14 citiesaround the worldare shown (The Weather
Channel, April $22,2009 ) .$
a. What is the sample mean high temperature?
b. What is the sample mean low temperature?
c. What is the correlation between the high and low temperatures? Discuss.

Tim Schmuhl

Numerade Educator

Problem 52

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.

Zach Steedman

Numerade Educator

Problem 53

Consider the sample data in the following frequency distribution.
a. Compute the sample mean.
b. Compute the sample variance and sample standard deviation.

Tim Schmuhl

Numerade Educator

Problem 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 $\mathrm{A}, 15$ credit hours of $\mathrm{B}, 33$ credit hours of $\mathrm{C},$ and 3 credit hours of $\mathrm{D}$
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?

Zach Steedman

Numerade Educator

Problem 55

Morning star tracks the total return for a large number of mutual funds. The following table shows the total return and the number of funds for four categories of mutual funds (Morning star Funds $500,2008 ) .$
a. Using the number of funds as weights, compute the weighted average total return for the mutual funds covered by Morning star.
b. Is there any difficulty associated with using the "number of funds's" as the weights in computing the weighted average total return for Morning star in part (a)? Discuss. What else might be used for weights?
c. Suppose you had invested $\$ 10,000$ in mutual funds at the beginning of 2007 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?

HC

Haoyu Chen

Numerade Educator

Problem 56

Based on a survey of 425 master's programs in business administration, the 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 below to compute the weighted mean score for the business school deans and the corporate recruiters. Discuss.

Zach Steedman

Numerade Educator

Problem 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.

Tim Schmuhl

Numerade Educator

Problem 58

According to an annual consumer spending survey, the average monthly Bank of America
Visa credit card charge was $\$ 1838(U . S .$ Airways Attache Magazine, December 2003$) . \mathrm{A}$ sample of monthly credit card charges provides the following data.
$$\begin{array}{ccccc}{236} & {1710} & {1351} & {825} & {7450} \\ {316} & {4135} & {1333} & {1584} & {387} \\ {991} & {3396} & {170} & {1428} & {1688}\end{array}$$
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 distribu-
tion. Is it the shape you would expect? Why or why not?
f. Do the data contain outliers?

Zach Steedman

Numerade Educator

Problem 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 quatiles 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?

Tim Schmuhl

Numerade Educator

Problem 60

Dividend yield is the annual dividend per share a company pays divided by the current mar-
ket 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?

Zach Steedman

Numerade Educator

Problem 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.
$$\begin{array}{llllllll}{10.1} & {14.8} & {5.0} & {10.2} & {12.4} & {12.2} & {2.0} & {11.5} & {17.8} & {4.0}\end{array}$$
a. For those students who use a student loan, what is the mean loan debt upon graduation?
b. What is the variance? Standard deviation?

Tim Schmuhl

Numerade Educator

Problem 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?

Zach Steedman

Numerade Educator

Problem 63

Publictransportation and theautomobile aretwomethodsan employeecan useto getto work
each day. Samples of times recorded for each method are shown. Times are in minutes.
$$\begin{array}{lllllllll}{\text { Public Transportation: }} & { 28} & {29} & {32} & {37} & {33} & {25} & {29} & {32} & {41} & {34} \\ {\text {Automobile:}} & {29} & {31} & {33} & {32} & {34} & {30} & {31} & {32} & {35} & {33}\end{array}$$
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 $(\mathrm{c}) ?$

Tim Schmuhl

Numerade Educator

Problem 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.
$$\begin{array}{cccccc}{995.9} & {48.8} & {175.0} & {263.5} & {298.0} & {218.9} & {209.0} \\ {628.3} & {111.0} & {212.9} & {92.6} & {2325.0} & {958.0} & {212.5}\end{array}$$
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 outtliers?
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?

Zach Steedman

Numerade Educator

Problem 65

The U.S. Census Bureau's American Community Survey reported the percentage of
children under 18 years of age who had lived below the poverty level during the previous
12 months (U.S. Census Bureau website, August $2008 ) .$ The region of the country, Northeast (NE), Southeast (SE), Midwest (MW), Southwest (SW), and West (W) and the
percentage of children under 18 who had lived below the poverty level are shown for
each state.
a. What is the median poverty level percentage for the 50 states?
b. What are the first and third quartiles? What is your interpretation of the quartiles?
c. Show a box plot for the data. Interpret the box plot in terms of what it tells you about
the level of poverty for children in the United States. Are any states considered out-
liers? Discuss.
d. Identify the states in the lower quartile. What is your interpretation of this group and
what region or regions are represented most in the lower quartile?

Tim Schmuhl

Numerade Educator

Problem 66

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 relation-
ship between the number of rooms and the cost per night for a double room? Does this
appear reasonable? Discuss.

Zach Steedman

Numerade Educator

Problem 67

Morningstar tracks the performance of a large number of companies and publishes an eval-
uation of each. Along with a variety of financial data, Morningstar includes a Fair Value
estimate for the price that should be paid for a share of the company's common stock. Data
for 30 companies are available in the file named Fair Value. The data include the Fair Value
estimate per share of common stock, the most recent price per share, and the earning per
share for the company (Morningstar Stocks $500,2008 ) .$
a. Develop a scatter diagram for the Fair Value and Share Price data with Share Price on the horizontal axis. What is the sample correlation coefficient, and what can you say
about the relationship between the variables?
b. Develop a scatter diagram for the Fair Value and Earnings per Share data with Eam-
ings per Share on the horizontal axis. What is the sample correlation coefficient, and
what can you say about the relationship between the variables?

Paul A.

California State Polytechnic University, Pomona

Problem 68

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 training indicating how
the team will play during the regular season? What are some of the reasons why this
occurs? Discuss.

Zach Steedman

Numerade Educator

Problem 69

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.

Khalida Dawar

Numerade Educator

Problem 70

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.

Zach Steedman

Numerade Educator