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Business Analytics

Jeffrey D. Camm, James J. Cochran, Michael J. Fry, Jeffrey W. Ohlmann, David R. Anderson, Dennis J. Sweeney, Thomas A. Williams

Chapter 2

Descriptive Statistics - all with Video Answers

Educators


Chapter Questions

02:49

Problem 1

A Wall Street Journal subscriber survey asked 46 questions about subscriber characteristics and interests. State whether each of the following questions provides categorical or quantitative data.
a. What is your age?
b. Are you male or female?
c. When did you first start reading the WSJ? High school, college, early career, midcareer, late career, or retirement?
d. How long have you been in your present job or position?
e. What type of vehicle are you considering for your next purchase? Nine response categories include sedan, sports car, SUV, minivan, and so on.

Dominador Tan
Dominador Tan
Numerade Educator
06:08

Problem 2

The following table contains a partial list of countries, the continents on which they are located, and their respective gross domestic products (GDP) in U.S. dollars. A list of 125 countries and their GDPs is contained in the file GDPlist.
$$
\begin{array}{llr}
\text { Country } & \text { Continent } & \text { GDP (millions of US\$) } \\
\text { Afghanistan } & \text { Asia } & 18,181 \\
\text { Albania } & \text { Europe } & 12,847 \\
\text { Algeria } & \text { Africa } & 190,709 \\
\text { Angola } & \text { Africa } & 100,948 \\
\text { Argentina } & \text { South America } & 447,644 \\
\text { Australia } & \text { Oceania } & 1,488,221 \\
\text { Austria } & \text { Europe } & 419,243 \\
\text { Azerbaijan } & \text { Europe } & 62,321 \\
\text { Bahrain } & \text { Asia } & 26,108 \\
\text { Bangladesh } & \text { Asia } & 113,032 \\
\text { Belarus } & \text { Europe } & 55,483 \\
\text { Belgium } & \text { Europe } & 513,396 \\
\text { Bolivia } & \text { South America } & 24,604 \\
\text { Bosnia and Herzegovina } & \text { Europe } & 17,965 \\
\text { Botswana } & \text { Africa } & 17,570
\end{array}
$$
a. Sort the countries in GDPlist from largest to smallest GDP. What are the top 10 countries according to GDP?
b. Filter the countries to display only the countries located in Africa. What are the top 5 countries located in Africa according to GDP?
c. What are the top 5 countries by GDP that are located in Europe?

Oluwadamilola Ameobi
Oluwadamilola Ameobi
Numerade Educator

Problem 3

Ohio Logistics manages the logistical activities for firms by matching companies that need products shipped with carriers that can provide the best rates and best service for the companies. Ohio Logistics is very concerned that its carriers deliver their customers' material on time, so it carefully monitors the percentage of on-time deliveries. The following table contains a list of the carriers used by Ohio Logistics and the corresponding on-time percentages for the current and previous years.
$$
\begin{array}{lcc}
\text { Carrier } & \begin{array}{c}
\text { Previous Year On-Time } \\
\text { Deliveries (\%) }
\end{array} & \begin{array}{c}
\text { Current Year On-Time } \\
\text { Deliveries (\%) }
\end{array} \\
\text { Blue Box Shipping } & 88.4 & 94.8 \\
\text { Cheetah LLC } & 89.3 & 91.8 \\
\text { Granite State Carriers } & 81.8 & 87.6 \\
\text { Honsin Limited } & 74.2 & 80.1
\end{array}
$$
$$
\begin{array}{|c|c|c|}
\hline \text { Carrier } & \begin{array}{l}
\text { Previous Year On-Time } \\
\text { Deliveries (\%) }
\end{array} & \begin{array}{l}
\text { Current Year On-Time } \\
\text { Deliveries (\%) }
\end{array} \\
\hline \text { Jones Brothers } & 68.9 & 82.8 \\
\hline \text { Minuteman Company } & 91.0 & 84.2 \\
\hline \text { Rapid Response } & 78.8 & 70.9 \\
\hline \text { Smith Logistics } & 84.3 & 88.7 \\
\hline \text { Super Freight } & 92.1 & 86.8 \\
\hline
\end{array}
$$
a. Sort the carriers in descending order by their current year's percentage of on-time deliveries. Which carrier is providing the best service in the current year? Which carrier is providing the worst service in the current year?
b. Calculate the change in percentage of on-time deliveries from the previous to the current year for each carrier. Use Excel's conditional formatting to highlight the carriers whose on-time percentage decreased from the previous year to the current year.
c. Use Excel's conditional formatting tool to create data bars for the change in percentage of on-time deliveries from the previous year to the current year for each carrier calculated in part $b$.
d. Which carriers should Ohio Logistics try to use in the future? Why?

Check back soon!
09:27

Problem 4

A partial relative frequency distribution is given.
$$
\begin{array}{cc}
\text { Class } & \text { Relative Frequency } \\
\text { A } & 0.22 \\
\text { B } & 0.18 \\
\text { C } & 0.40 \\
\text { D } &
\end{array}
$$
a. What is the relative frequency of class $\mathrm{D}$ ?
b. The total sample size is 200 . What is the frequency of class $\mathrm{D}$ ?
c. Show the frequency distribution.
d. Show the percent frequency distribution.

Mihir Nayar
Mihir Nayar
Numerade Educator
View

Problem 5

In a recent report, the top five most-visited English-language web sites were google. com (GOOG), facebook.com (FB), youtube.com (YT), yahoo.com (YAH), and wikipedia.com (WIKI). The most-visited web sites for a sample of 50 Internet users are shown in the following table:
$$
\begin{array}{lllll}
\text { YAH } & \text { WIKI } & \text { YT } & \text { WIKI } & \text { GOOG } \\
\text { YT } & \text { YAH } & \text { GOOG } & \text { GOOG } & \text { GOOG } \\
\text { WIKI } & \text { GOOG } & \text { YAH } & \text { YAH } & \text { YAH } \\
\text { YAH } & \text { YT } & \text { GOOG } & \text { YT } & \text { YAH } \\
\text { GOOG } & \text { FB } & \text { FB } & \text { WIKI } & \text { GOOG } \\
\text { GOOG } & \text { GOOG } & \text { FB } & \text { FB } & \text { WIKI } \\
\text { FB } & \text { YAH } & \text { YT } & \text { YAH } & \text { YAH } \\
\text { YT } & \text { GOOG } & \text { YAH } & \text { FB } & \text { FB } \\
\text { WIKI } & \text { GOOG } & \text { YAH } & \text { WIKI } & \text { WIKI } \\
\text { YAH } & \text { YT } & \text { GOOG } & \text { GOOG } & \text { WIKI }
\end{array}
$$
a. Are these data categorical or quantitative?
b. Provide frequency and percent frequency distributions.
c. On the basis of the sample, which web site is most frequently the most-often-visited web site for Internet users? Which is second?

Rashmi Sinha
Rashmi Sinha
Numerade Educator
02:59

Problem 6

In a study of how chief executive officers (CEOs) spend their days, it was found that CEOs spend an average of about 18 hours per week in meetings, not including conference calls, business meals, and public events. Shown here are the times spent per week in meetings (hours) for a sample of 25 CEOs:
$$
\begin{array}{lllll}
14 & 15 & 18 & 23 & 15 \\
19 & 20 & 13 & 15 & 23 \\
23 & 21 & 15 & 20 & 21 \\
16 & 15 & 18 & 18 & 19 \\
19 & 22 & 23 & 21 & 12
\end{array}
$$
a. What is the least amount of time a CEO spent per week in meetings in this sample? The highest?
b. Use a class width of 2 hours to prepare a frequency distribution and a percent frequency distribution for the data.
c. Prepare a histogram and comment on the shape of the distribution.

Jorge Villanueva
Jorge Villanueva
Numerade Educator
03:15

Problem 7

Consumer complaints are frequently reported to the Better Business Bureau. Industries with the most complaints to the Better Business Bureau are often banks, cable and satellite television companies, collection agencies, cellular phone providers, and new car dealerships. The results for a sample of 200 complaints are in the file $B B B$.
a. Show the frequency and percent frequency of complaints by industry.
b. Which industry had the highest number of complaints?
c. Comment on the percentage frequency distribution for complaints.

Jorge Villanueva
Jorge Villanueva
Numerade Educator
08:07

Problem 8

Reports have found that many U.S. adults would rather live in a different type of community than the one in which they are living now. A national survey of 2,260 adults asked: "Where do you live now?" and "What do you consider to be the ideal community?" Response options were City (C), Suburb (S), Small Town (T), or Rural (R). A representative portion of this survey for a sample of 100 respondents is as follows:
$$
\begin{aligned}
&\text { Where do you live now? }\\
&\begin{array}{lllllllllllllll}
\mathrm{S} & \mathrm{T} & \mathrm{R} & \mathrm{C} & \mathrm{R} & \mathrm{R} & \mathrm{T} & \mathrm{C} & \mathrm{S} & \mathrm{T} & \mathrm{C} & \mathrm{S} & \mathrm{C} & \mathrm{S} & \mathrm{T} \\
\mathrm{S} & \mathrm{S} & \mathrm{C} & \mathrm{S} & \mathrm{S} & \mathrm{T} & \mathrm{T} & \mathrm{C} & \mathrm{C} & \mathrm{S} & \mathrm{T} & \mathrm{C} & \mathrm{S} & \mathrm{T} & \mathrm{C} \\
\mathrm{T} & \mathrm{R} & \mathrm{S} & \mathrm{S} & \mathrm{T} & \mathrm{C} & \mathrm{S} & \mathrm{C} & \mathrm{T} & \mathrm{C} & \mathrm{T} & \mathrm{C} & \mathrm{T} & \mathrm{C} & \mathrm{R} \\
\mathrm{C} & \mathrm{C} & \mathrm{R} & \mathrm{T} & \mathrm{C} & \mathrm{S} & \mathrm{S} & \mathrm{T} & \mathrm{S} & \mathrm{C} & \mathrm{C} & \mathrm{C} & \mathrm{R} & \mathrm{S} & \mathrm{C} \\
\mathrm{S} & \mathrm{S} & \mathrm{C} & \mathrm{C} & \mathrm{S} & \mathrm{C} & \mathrm{R} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{C} & \mathrm{R} & \mathrm{T} & \mathrm{C} & \mathrm{R} \\
\mathrm{C} & \mathrm{T} & \mathrm{R} & \mathrm{R} & \mathrm{C} & \mathrm{T} & \mathrm{C} & \mathrm{C} & \mathrm{R} & \mathrm{T} & \mathrm{T} & \mathrm{R} & \mathrm{S} & \mathrm{R} & \mathrm{T} \\
\mathrm{T} & \mathrm{S} & \mathrm{S} & \mathrm{S} & \mathrm{S} & \mathrm{S} & \mathrm{C} & \mathrm{C} & \mathrm{R} & \mathrm{T} & & & & &
\end{array}
\end{aligned}
$$
$$
\begin{aligned}
&\text { What do you consider to be the ideal community? }\\
&\begin{array}{lllllllllllllll}
\mathrm{S} & \mathrm{C} & \mathrm{R} & \mathrm{R} & \mathrm{R} & \mathrm{S} & \mathrm{T} & \mathrm{S} & \mathrm{S} & \mathrm{T} & \mathrm{T} & \mathrm{S} & \mathrm{C} & \mathrm{S} & \mathrm{T} \\
\mathrm{C} & \mathrm{C} & \mathrm{R} & \mathrm{T} & \mathrm{R} & \mathrm{S} & \mathrm{T} & \mathrm{T} & \mathrm{S} & \mathrm{S} & \mathrm{C} & \mathrm{C} & \mathrm{T} & \mathrm{T} & \mathrm{S} \\
\mathrm{S} & \mathrm{R} & \mathrm{C} & \mathrm{S} & \mathrm{C} & \mathrm{C} & \mathrm{S} & \mathrm{C} & \mathrm{R} & \mathrm{C} & \mathrm{T} & \mathrm{S} & \mathrm{R} & \mathrm{R} & \mathrm{R} \\
\mathrm{C} & \mathrm{T} & \mathrm{S} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{R} & \mathrm{R} & \mathrm{S} & \mathrm{C} & \mathrm{C} & \mathrm{R} & \mathrm{R} & \mathrm{S} & \mathrm{S} \\
\mathrm{S} & \mathrm{T} & \mathrm{C} & \mathrm{T} & \mathrm{T} & \mathrm{C} & \mathrm{R} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{C} & \mathrm{T} & \mathrm{T} & \mathrm{R} & \mathrm{R} \\
\mathrm{C} & \mathrm{S} & \mathrm{R} & \mathrm{T} & \mathrm{C} & \mathrm{T} & \mathrm{C} & \mathrm{C} & \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{R} & \mathrm{C} & \mathrm{R} & \mathrm{T} \\
\mathrm{T} & \mathrm{C} & \mathrm{S} & \mathrm{S} & \mathrm{C} & \mathrm{S} & \mathrm{T} & \mathrm{S} & \mathrm{S} & \mathrm{R} & & & & &
\end{array}
\end{aligned}
$$
Develop frequency and percent frequency distributions for the data above to answer the following questions.
a. Where are most adults living now?
b. Where do most adults consider the ideal community to be?
c. What changes in living areas would you expect to see if people moved from where they currently live to their ideal community?

Pratyush Raitan
Pratyush Raitan
Numerade Educator
03:27

Problem 9

Consider the following data:
$$
\begin{array}{llll}
14 & 24 & 18 & 22 \\
19 & 18 & 16 & 22 \\
24 & 17 & 15 & 16 \\
19 & 23 & 24 & 16 \\
16 & 26 & 21 & 16 \\
20 & 22 & 16 & 12 \\
24 & 23 & 19 & 25 \\
20 & 25 & 21 & 19 \\
21 & 25 & 23 & 24 \\
22 & 19 & 20 & 20
\end{array}
$$
a. Develop a frequency distribution using classes of $12-14,15-17,18-20,21-23$, and 24-26.
b. Develop a relative frequency distribution and a percent frequency distribution using the classes in part a.

Jerelyn Nevil
Jerelyn Nevil
Numerade Educator
02:32

Problem 10

Consider the following frequency distribution.
$$
\begin{array}{lc}
\text { Class } & \text { Frequency } \\
10-19 & 10 \\
20-29 & 14 \\
30-39 & 17 \\
40-49 & 7 \\
50-59 & 2
\end{array}
$$
Construct a cumulative frequency distribution.

Jerelyn Nevil
Jerelyn Nevil
Numerade Educator
07:23

Problem 11

The owner of an automobile repair shop studied the waiting times for customers who arrive at the shop for an oil change. The following data with waiting times in minutes were collected over a one-month period.
$\begin{array}{llllllllllllllllllll}2 & 5 & 10 & 12 & 4 & 4 & 5 & 17 & 11 & 8 & 9 & 8 & 12 & 21 & 6 & 8 & 7 & 13 & 18 & 3\end{array}$
Using classes of $0-4,5-9$, and so on, show the following:
a. The frequency distribution
b. The relative frequency distribution
c. The cumulative frequency distribution
d. The cumulative relative frequency distribution
e. The proportion of customers needing an oil change who wait 9 minutes or less.

Pratyush Raitan
Pratyush Raitan
Numerade Educator
08:58

Problem 12

Approximately 1.65 million high school students take the Scholastic Aptitude Test (SAT) each year, and nearly $80 \%$ of the college and universities without open admissions policies use SAT scores in making admission decisions. The current version of the SAT includes three parts: reading comprehension, mathematics, and writing. A perfect combined score for all three parts is 2400 . A sample of SAT scores for the combined three-part SAT are as follows:
$$
\begin{array}{lllll}
1665 & 1525 & 1355 & 1645 & 1780 \\
1275 & 2135 & 1280 & 1060 & 1585 \\
1650 & 1560 & 1150 & 1485 & 1990 \\
1590 & 1880 & 1420 & 1755 & 1375 \\
1475 & 1680 & 1440 & 1260 & 1730 \\
1490 & 1560 & 940 & 1390 & 1175
\end{array}
$$
a. Show a frequency distribution and histogram. Begin with the first bin starting at 800 , and use a bin width of 200 .
b. Comment on the shape of the distribution.
c. What other observations can be made about the SAT scores based on the tabular and graphical summaries?

Mihir Nayar
Mihir Nayar
Numerade Educator
01:38

Problem 13

Consider a sample with data values of $10,20,12,17$, and 16 .
a. Compute the mean and median.
b. Consider a sample with data values $10,20,12,17,16$, and 12 . How would you expect the mean and median for these sample data to compare to the mean and median for part a (higher, lower, or the same)? Compute the mean and median for the sample data $10,20,12,17,16$, and 12 .

AY
Aria Ye
Numerade Educator
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Problem 14

Consider a sample with data values of $27,25,20,15,30,34,28$, and 25 . Compute the 20th, 25 th, 65 th, and 75 th percentiles.

Jason Gerber
Jason Gerber
Numerade Educator
02:59

Problem 15

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
Megha Nayar
Numerade Educator
00:29

Problem 16

If an asset declines in value from $$\$ 5,000$$ to $$\$ 3,500$$ over nine years, what is the mean annual growth rate in the asset's value over these nine years?

Sanchit Gogia
Sanchit Gogia
Numerade Educator
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Problem 17

Suppose that you initially invested $$\$ 10,000$$ in the Stivers mutual fund and $$\$ 5,000$$ in the Trippi mutual fund. The value of each investment at the end of each subsequent year is provided in the table:
$$
\begin{array}{ccc}
\text { Year } & \text { Stivers (\$) } & \text { Trippi (\$) } \\
1 & 11,000 & 5,600 \\
2 & 12,000 & 6,300 \\
3 & 13,000 & 6,900 \\
4 & 14,000 & 7,600 \\
5 & 15,000 & 8,500 \\
6 & 16,000 & 9,200 \\
7 & 17,000 & 9,900 \\
8 & 18,000 & 10,600
\end{array}
$$
Which of the two mutual funds performed better over this time period?

Jason Gerber
Jason Gerber
Numerade Educator
06:08

Problem 18

The average time that Americans commute to work is 27.7 minutes (Sterling's Best Places, April 13, 2012). The average commute times in minutes for 48 cities are as follows:
$$
\begin{array}{llllll}
\text { Albuquerque } & 23.3 & \text { Jacksonville } & 26.2 & \text { Phoenix } & 28.3 \\
\text { Atlanta } & 28.3 & \text { Kansas City } & 23.4 & \text { Pittsburgh } & 25.0 \\
\text { Austin } & 24.6 & \text { Las Vegas } & 28.4 & \text { Portland } & 26.4 \\
\text { Baltimore } & 32.1 & \text { Little Rock } & 20.1 & \text { Providence } & 23.6 \\
\text { Boston } & 31.7 & \text { Los Angeles } & 32.2 & \text { Richmond } & 23.4 \\
\text { Charlotte } & 25.8 & \text { Louisville } & 21.4 & \text { Sacramento } & 25.8 \\
\text { Chicago } & 38.1 & \text { Memphis } & 23.8 & \text { Salt Lake City } & 20.2 \\
\text { Cincinnati } & 24.9 & \text { Miami } & 30.7 & \text { San Antonio } & 26.1 \\
\text { Cleveland } & 26.8 & \text { Milwaukee } & 24.8 & \text { San Diego } & 24.8 \\
\text { Columbus } & 23.4 & \text { Minneapolis } & 23.6 & \text { San Francisco } & 32.6 \\
\text { Dallas } & 28.5 & \text { Nashville } & 25.3 & \text { San Jose } & 28.5 \\
\text { Denver } & 28.1 & \text { New Orleans } & 31.7 & \text { Seattle } & 27.3 \\
\text { Detroit } & 29.3 & \text { New York } & 43.8 & \text { St. Louis } & 26.8 \\
\text { El Paso } & 24.4 & \text { Oklahoma City } & 22.0 & \text { Tucson } & 24.0 \\
\text { Fresno } & 23.0 & \text { Orlando } & 27.1 & \text { Tulsa } & 20.1 \\
\text { Indianapolis } & 24.8 & \text { Philadelphia } & 34.2 & \text { Washington, D.C. } & 32.8
\end{array}
$$
a. What is the mean commute time for these 48 cities?
b. What is the median commute time for these 48 cities?
c. What is the mode for these 48 cities?
d. What is the variance and standard deviation of commute times for these 48 cities?
e. What is the third quartile of commute times for these 48 cities?

Jon Southam
Jon Southam
Numerade Educator
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Problem 19

Suppose that the average waiting time for a patient at a physician's office is just over 29 minutes. 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 (in minutes) for a sample of patients at offices that do not have a wait-tracking system and wait times for a sample of patients at offices with such systems.
$$
\begin{array}{cc}
\text { Without Wait-Tracking System } & \text { With Wait-Tracking System } \\
24 & 31 \\
67 & 11 \\
17 & 14 \\
20 & 18 \\
31 & 12 \\
44 & 37 \\
12 & 9 \\
23 & 13 \\
16 & 12 \\
37 & 15
\end{array}
$$
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. Create a box plot for patient wait times for offices without a wait-tracking system.
d. Create a box plot for patient wait times for offices with a wait-tracking system.
e. Do offices with a wait-tracking system have shorter patient wait times than offices without a wait-tracking system? Explain.

Jason Gerber
Jason Gerber
Numerade Educator
03:16

Problem 20

According to the National Education Association (NEA), teachers generally spend more than 40 hours each week working on instructional duties. 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.
$\begin{array}{llllllllllllll}\text { High school science teachers } & 53 & 56 & 54 & 54 & 55 & 58 & 49 & 61 & 54 & 54 & 52 & 53 & 54\end{array}$
$\begin{array}{llllllllllll}\text { High school English teachers } & 52 & 47 & 50 & 46 & 47 & 48 & 49 & 46 & 55 & 44 & 47\end{array}$
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. Create a box plot for the number of hours worked for high school science teachers.
d. Create a box plot for the number of hours worked for high school English teachers.
e. Comment on the differences between the box plots for science and English teachers.

Nick Johnson
Nick Johnson
Numerade Educator
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Problem 21

Return to the waiting times given for the physician's office in Problem 19.
a. Considering only offices without a wait-tracking system, what is the $z$-score for the 10th patient in the sample (wait time $=37$ minutes)?
b. Considering only offices with a wait-tracking system, what is the $z$-score for the 6 th patient in the sample (wait time $=37$ minutes)? How does this $z$-score compare with the $z$-score you calculated for part a?
c. 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 without a wait-tracking system contain any outliers?

Jason Gerber
Jason Gerber
Numerade Educator
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Problem 22

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 and that the number of hours of sleep follows a bell-shaped distribution.
a. Use the empirical rule to calculate the percentage of individuals who sleep between 4.5 and 9.3 hours per day.
b. What is the $z$-value for an adult who sleeps 8 hours per night?
c. What is the $z$-value for an adult who sleeps 6 hours per night?

Jason Gerber
Jason Gerber
Numerade Educator
07:10

Problem 23

Suppose that the national average for the math portion of the College Board's SAT is 515 . 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 math 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 is the $z$-score for student with an SAT math score of 620 ?
e. What is the $z$-score for a student with an SAT math score of 405 ?

DC
Dominic Chaulk
Numerade Educator
03:12

Problem 24

Five observations taken for two variables follow.
$$
\begin{array}{r|rrrrr}
x_i & 4 & 6 & 11 & 3 & 16 \\
\hline y_i & 50 & 50 & 40 & 60 & 30
\end{array}
$$
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.

Nick Johnson
Nick Johnson
Numerade Educator
11:12

Problem 25

The scatter chart in the following figure was created using sample data for profits and market capitalizations from a sample of firms in the Fortune 500 .
a. Discuss what the scatter chart indicates about the relationship between profits and market capitalization?
b. The data used to produce this are contained in the file Fortune500. Calculate the covariance between profits and market capitalization. Discuss what the covariance indicates about the relationship between profits and market capitalization?
c. Calculate the correlation coefficient between profits and market capitalization. What does the correlations coefficient indicate about the relationship between profits and market capitalization?

Paul A.
Paul A.
California State Polytechnic University, Pomona
03:42

Problem 26

The economic downturn in 2008-2009 resulted in the loss of jobs and an increase in delinquent loans for housing. 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 following data show the jobless rate and the delinquent loan percentage for 27 major real estate markets.
$$
\begin{array}{lcclcc}
\text { Metro Area } & \begin{array}{c}
\text { Jobless } \\
\text { Rate (\%) }
\end{array} & \begin{array}{c}
\text { Delinquent } \\
\text { Loans (\%) }
\end{array} & \begin{array}{l}
\text { Metro Area }
\end{array} & \begin{array}{c}
\text { Jobless } \\
\text { Rate (\%) }
\end{array} & \begin{array}{c}
\text { Delinquent } \\
\text { Loans (\%) }
\end{array} \\
\text { Atlanta } & 7.1 & 7.02 & \text { New York } & 6.2 & 5.78 \\
\text { Boston } & 5.2 & 5.31 & \text { Orange County } & 6.3 & 6.08 \\
\text { Charlotte } & 7.8 & 5.38 & \text { Orlando } & 7.0 & 10.05 \\
\text { Chicago } & 7.8 & 5.40 & \text { Philadelphia } & 6.2 & 4.75 \\
\text { Dallas } & 5.8 & 5.00 & \text { Phoenix } & 5.5 & 7.22 \\
\text { Denver } & 5.8 & 4.07 & \text { Portland } & 6.5 & 3.79 \\
\text { Detroit } & 9.3 & 6.53 & \text { Raleigh } & 6.0 & 3.62 \\
\text { Houston } & 5.7 & 5.57 & \text { Sacramento } & 8.3 & 9.24 \\
\text { Jacksonville } & 7.3 & 6.99 & \text { St. Louis } & 7.5 & 4.40 \\
\text { Las Vegas } & 7.6 & 11.12 & \text { San Diego } & 7.1 & 6.91 \\
\text { Los Angeles } & 8.2 & 7.56 & \text { San Francisco } & 6.8 & 5.57 \\
\text { Miami } & 7.1 & 12.11 & \text { Seattle } & 5.5 & 3.87 \\
\text { Minneapolis } & 6.3 & 4.39 & \text { Tampa } & 7.5 & 8.42 \\
\text { Nashville } & 6.6 & 4.78 & & &
\end{array}
$$
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 the jobless rate and the percentage of delinquent housing loans.

Tim Schmuhl
Tim Schmuhl
Numerade Educator
05:05

Problem 27

Huron Lakes Candies (HLC) has developed a new candy bar called Java Cup that is a milk chocolate cup with a coffee-cream center. In order to assess the market potential of Java Cup, HLC has developed a taste test and follow-up survey. Respondents were asked to taste Java Cup and then rate Java Cup's taste, texture, creaminess of filling, sweetness, and depth of the chocolate flavor of the cup on a 100 -point scale. The taste test and survey were administered to 217 randomly selected adult consumers. Data collected from each respondent are provided in the file JavaCup.
a. Are there any missing values in HLC's survey data? If so, identify the respondents for which data are missing and which values are missing for each of these respondents.
b. Are there any values in HLC's survey data that appear to be erroneous? If so, identify the respondents for which data appear to be erroneous and which values appear to be erroneous for each of these respondents.

Sheryl Ezze
Sheryl Ezze
Numerade Educator

Problem 28

Marilyn Marshall, a Professor of sports economics, has obtained a data set of home attendance for each of the 30 major league baseball franchises for each season from 2010 through 2016. Dr. Marshall suspects the data, provided in the file AttendMLB, is in need of a thorough cleansing. You should also find a reliable source of Major League Baseball attendance for each franchise between 2010 and 2016 to use to help you identify appropriate imputation values for data missing in the AttendMLB file.
a. Are there any missing values in Dr. Marshall's data? If so, identify the teams and seasons for which data are missing and which values are missing for each of these teams and seasons. Use the reliable source of Major League Baseball Attendance for each franchise between 2010 and 2016 you have found to find the correct value in each instance.
b. Are there any values in Dr. Marshall's data that appear to be erroneous? If so, identify the teams and seasons for which data appear to be erroneous and which values appear to be erroneous for each of these teams and seasons. Use the reliable source of Major League Baseball Attendance for each franchise between 2010 and 2016 you have found to find the correct value in each instance.

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