1(Q) Many service companies collect data via a follow-up survey of their customers. For example, to ascertain customer sentiment, Delta Air Lines sends an e-mail to customers immediately following a flight. Among other questions, Delta asks:

How likely are you to recommend Delta Air Lines to others?

a. Are the data collected by Delta in this example quantitative or categorical?

CATEGORIAL

b. What measurement scale is used?

ORDINAL

2. Refer to the data set in table as shown below:

Brand	Model	Price ($)	Overall Score	Voice Quality	Talk Time (hours)
AT&T	CL84100	60	73	Excellent	7
AT&T	TL92271	80	70	Very Good	7
Panasonic	4773B	100	78	Very Good	13
Panasonic	6592T	70	72	Very Good	13
Uniden	D2997	45	70	Very Good	10
Uniden	D1788	80	73	Very Good	7
Vtech	DS6521	60	72	Excellent	7
Vtech	CS6649	50	72	Very Good	7

a. What is the average price for the phones (to 2 decimals)?

68.12

b. What is the average talk time for the phones (to 3 decimals)?

8.875

c. What percentage of the phones have a voice quality of excellent (to the nearest whole number)?

3. Based on data from the U.S. Census Bureau, a Pew Research study showed that the percentage of employed individuals ages 25-29 who are college educated is at an all-time high. The study showed that the percentage of employed individuals aged 25-29 with at least a bachelor’s degree in 2016 was 40% . In the year 200 , this percentage was , in it was 32% , in 1985 it Was 25%, and in 1964 it was only 16% (Pew Research website).

a. What is the population being studied in each of the four years in which Pew has data?

Employed individuals in the U.S. aged 25-29

b. What question was posed to each respondent?

Have you earned a bachelor’s degree (or higher)?

c. Do responses to the question provide categorical or quantitative data?

Categorical

4. A Gallup Poll utilizing a random sample of 1,503 adults ages 18 or older was conducted in April 2018 . The survey indicated a majority of Americans (53%) say driverless cars will be common in the next 10 years (Gallup, https://news.gallup.com/poll/234152/americans-expect-driverless-cars-common-next-decade.aspx). The question asked was:

Thinking about fully automated, “driverless cars,” cars that use technology to drive and do not need a human driver, based on what you have heard or read, how soon do you think driverless cars will be commonly used in the [United States]?

The figure below shows a summary of results of the survey in a histogram indicating the percentage of the total responses in different time intervals.

a. Are the responses to the survey question quantitative or categorical?

Quantitative

b. How many of the respondents said that they expect driverless cars to be common in the next 10 years? Round your answer to nearest whole number.

797

c. How many respondents answered in the range 16-20 years? Round your answer to nearest whole number.

151

5. A seven-year medical research study reported that women whose mothers took the drug DES during pregnancy were twice as likely to develop tissue abnormalities that might lead to cancer as were women whose mothers did not take the drug.

a. This study compared two populations. What were the populations?

Women whose mothers took DES during pregnancy and women whose mothers did not.

b. Do you suppose the data were obtained in a survey or in an experiment?

Survey

c. For the population of women whose mothers took the drug DES during pregnancy, a sample of 3980 women showed that 63 developed tissue abnormalities that might lead to cancer. Provide a descriptive statistic (to 1 decimal) that could be used to estimate the number of women out of 1000 in this population who have tissue abnormalities.

15.8

d. For the population of women whose mothers did not take the drug DES during pregnancy, what is the estimate (to 1 decimal) of the number of women out of 1000 who would be expected to have tissue abnormalities? (Hint: remember that women whose mothers took the drug were twice as likely to develop tissue abnormalities.)

7.9

e. True or false: Medical studies often use a relatively large sample (in this case, 3980) because disease occurrences can be rare and difficult to observe when only isolated populations are considered.

true

6. Consumer Reports evaluates products for consumers. The file CompactSUV (click on the datafile logo to reference the data) contains the data shown in the table below for 15 compact sports utility vehicles (SUVs) from the 2018 model line (Consumer Reports website):

Make — manufacturer

Model — name of the model

Overall score — awarded based on a variety of measures, including those in this data set

Recommended — Consumer Reports recommends the vehicle or not

Owner satisfaction — satisfaction on a five-point scale based on the percentage of owners who would purchase the vehicle again (——, —,0 , +, ++)

Overall miles per gallon — miles per gallon achieved in a 150-mile test trip

Acceleration ( 0—60 sec) — time in seconds it takes vehicle to reach miles per hour from a standstill with the engine idling

*Consumer Reports* Data Set for 15 Compact Sports Utility Vehicles
		Overall		Owner	Overall Miles	Acceleration
Make	Model	Score	Recommended	Satisfaction	per Gallon	(0–60) Sec
Subaru	Forester	84	Yes	+	26	8.7
Honda	CRV	83	Yes	++	27	8.6
Toyota	Rav4	81	Yes	++	24	9.3
Nissan	Rogue	73	Yes	+	24	9.5
Mazda	CX-5	71	Yes	++	24	8.6
Kia	Sportage	71	Yes	+	23	9.6
Ford	Escape	69	Yes	0	23	10.1
Volkswagen	Tiguan Limited	67	No	0	21	8.5
Volkswagen	Tiguan	65	No	+	25	10.3
Mitsubishi	Outlander	63	No	0	24	10.0
Chevrolet	Equinox	63	No	0	31	10.1
Hyundai	Tuscon	57	No	0	26	8.4
GMC	Terrain	57	No	0	22	7.2
Jeep	Cherokee	55	No	—	22	10.9
Jeep	Compass	50	No	0	24	9.8

a. How many variables are in the data set?

b. Which of the following variables are categorical, and which are quantitative?

Quantitative

Categorical

Quantitative

c. What percentage of these 15 vehicles are recommended? Round your answer to one decimal place.

46.6

d. What is the average of the overall miles per gallon across all 15 vehicles? Round your answer to one decimal place.

24.4

e. For owner satisfaction, select the bar chart.

Choose the correct bar graph from the above diagrams.

f. Show the frequency distribution for acceleration using the intervals: , , , and . Round your answers to the nearest whole number.

Acceleration
(0 — 60 sec)		Frequency
7.0 _ 7.9		1
8.0 _8.9		5
9.0 _ 9.9		4
10.0 _10.9		5

Choose the correct histogram from the above diagrams.

7. The response to a question has three alternatives: , , and . A sample of responses provides , , and . Show the frequency and relative frequency distributions (use 2 decimal for the relative frequency column).

Class	Frequency	Relative Frequency
A	66	0.55
B	24	0.2
C	30	0.25
Total	120	1

8. In alphabetical order, the six most common last names in the United States in 2018 were Brown, Garcia, Johnson, Jones, Smith, and Williams (United States Census Bureau website). Assume that a sample of individuals with one of these last names provided the following data. Click on the datafile logo to reference the data.

Brown	Williams	Williams	Williams	Brown
Smith	Jones	Smith	Johnson	Smith
Garcia	Smith	Brown	Williams	Johnson
Johnson	Smith	Smith	Johnson	Brown
Williams	Garcia	Johnson	Williams	Johnson
Williams	Johnson	Jones	Smith	Brown
Johnson	Smith	Smith	Brown	Jones
Jones	Jones	Smith	Smith	Garcia
Garcia	Jones	Williams	Garcia	Smith
Jones	Johnson	Brown	Johnson	Garcia

a. Fill in the frequency (to the whole number), the relative frequency (to 2 decimals), and percent frequency (to the whole number) values below.

Name	Frequency	Frequency	Frequency
Brown	7	0.14	14
Johnson	10	0.2	20
Jones	7	0.14	14
Garcia	6	0.12	12
Smith	12	0.24	24
Williams	8	0.16	16
Total:	50	1	100

b. Which of the following three bar charts accurately represents the data?

chart 1

c. Which of the following three sorted bar charts accurately represents the data?

chart 2

d. Select the correct pie chart from the following.

chart 2

e. Based on these data, what are the three most common last names?

Smith, Johnson, and Williams

Which type of chart makes this most apparent?

A sorted bar chart

9. Consider the following data. Click on the datafile logo to reference the data.

Summarize the data by filling in the frequency, the relative frequency (3 decimals), and the percent frequency (1 decimal) values below.

Frequency	Relative Frequency	Percent Frequency
2	0.05		5
8	0.20		20
11	0.275		27.5
10	0.25		25
9	0.225		22.5

40 1 100

10. Each year America.edu ranks the best paying college degrees in America. The following data show the median starting salary, the mid-career salary, and the percentage increase from starting salary to mid-career salary for the college degrees with the highest mid-career salary (America.edu website).

a. Using a class width of , select a histogram for the percentage increase in the starting salary.

Histogram 2

b. Comment on the shape of the distribution.

skewed to the right

c. Develop a stem-and-leaf display for the percentage increase in the starting salary. If your answer is “zero” enter “”.

4 3

5 1 3 7 9

7 1 3 4 5 7 7 9

8 2 4 7

9 0 3 6

10 0

11 3

d. What are the primary advantages of the stem-and-leaf display as compared to the histogram?

Easier to construct by hand and provides more information than the histogram.

11. According to The Wall Street Journal, a startup company’s ability to gain funding is a key to success. The funds raised (in millions of dollars) by startup companies follow. Click on the datafile logo to reference the data.

a. Construct a stem-and-leaf display. If your answer is “zero” enter “”.

1 8

2 0 1 4

3 1 8

4 0 0 7 8 9 9

5 0 1 2 4 4 4 5 7 8

6 0 0 1 3 9

7 2 3 7 8 8 8

8 0 1 1

9 1

10 3

11 0 2 8 9

12 9

13 0 1

15 4 6

16 6 8

19 2

27 2

b. Comment on the display.

less than

12. Western University has only one women’s softball scholarship remaining for the coming year. The final two players that Western is considering are Allison Fealey and Emily Janson. The coaching staff has concluded that the speed and defensive skills are virtually identical for the two players, and that the final decision will be based on which player has the best batting average. Crosstabulations of each player’s batting performance in their junior and senior years of high school are as follows:

0.375

0.35

0.30

0.291

allision fealey

b. Combine or aggregate the data for the junior and senior years into one crosstabulation as follows:

90 105

200 215

290 320

Calculate each player’s batting average for the combined two years.

0.3103

0.3281

Emily janson

c. Are the recommendations you made in parts (a) and (b) consistent? Explain any apparent inconsistencies.

The recommendations in parts (3) and (b) are not consistent. This is an example of Simpson’s Paradox.

13. Each year Forbes ranks the world’s most valuable brands. A portion of the data for of the brands in the Forbes list is shown in the table below (Forbes website). The data set includes the following variables:

10 4 1 0 0 0 15

7 5 0 0 0 0 12

11 3 0 0 0 0 14

14 10 0 2 0 0 26

7 4 0 1 1 2 15

49 26 1 3 1 2 82

b. Prepare a frequency distribution for the data on Industry.

c. Prepare a frequency distribution for the data on Brand Value ( billions).

d. How has the crosstabulation helped in preparing the frequency distributions in parts (b) and (c)?

frequency distribution for the fund type variable

Frequency distribution for the brand value

Higher

Technology

14. The Daytona 500 is a 500-mile automobile race held annually at the Daytona International Speedway in Daytona Beach, Florida. The following crosstabulation shows the automobile make by average speed of the 25 winners from 1988 to 2012 (The World Almanac).

a. Compute the row percentages. If required, round your answers to two decimal places. If your answer is “zero” enter “0”.

100.00 0.00 0.00 0.00 0.00 100.00

18.75 31.25 25.00 18.75 6.25 100.00

0.00 100.00 0.00 0.00 0.00 100.00

33.33 16.67 33.33 16.67 0.00 100.00

b. What percentage of winners driving a Chevrolet won with an average speed of at least miles per hour?

c. Compute the column percentages. If required, round your answers to two decimal places. If your answer is “zero” enter “0”.

16.67 0.00 0.00 0.00 0.00

50.00 62.50 66.67 75.00 100.00

0.00 25.00 0.00 0.00 0.00

33.33 12.50 33.33 25.00 0.00

100.00 100.00 100.00 100.0 100.0

d. What percentage of winning average speeds miles per hour were Chevrolets?

15. Consider a sample with data values of , , , , and . Round your answers to the nearest whole number.

Compute the mean.

Compute the median.

16. There is a severe shortage of critical care doctors and nurses to provide intensive-care services in hospitals. To offset this shortage, many hospitals, such as Emory Hospital in Atlanta, are using electronic intensive-care units (eICUs) to help provide this care to patients (Emory University News Center). eICUs use electronic monitoring tools and two-way communication through video and audio so that a centralized staff of specially trained doctors and nurses – who can be located as far away as Australia – can provide critical care services to patients located in remote hospitals without fully staffed ICUs. One of the most important metrics tracked by these eICUs is the time that a patient must wait for the first video interaction between the patient and the eICU staff. Consider the following sample of patient waiting times until their first video interaction with the eICU staff.

a. Compute the mean waiting time for these patients (to decimals).

43.825

b. Compute the median waiting time (to decimals).

c. Compute the mode (to decimal).

d. Compute the first and third quartiles (to decimals).

45.25

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. (to 2 decimals)

7.81

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?

choice i

c. Suppose you invested in this group of mutual funds and diversified the investment by placing in Domestic Equity funds, in International Equity funds, in Specialty Stock funds, and in Hybrid funds. What is the expected return on the portfolio? (to 2 decimals)

12.27

18. Annual revenue for Corning Supplies grew by in ; in ; in ; in ; and in .

What is the mean growth annual rate over this period? Round your answer to four decimal places. Do not round intermediate calculations.

0.7152

19. Consider a sample with data values of , , , , and .

Compute the range.

Compute the interquartile range (to decimal).

7.5

20. The following table displays round-trip flight prices from major U.S. cities to Atlanta and Salt Lake City.

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. Round your answers to two decimal places.

356.73

400.95

choice iii

b. Compute the range (round your answers to one decimal place), variance, and standard deviation (round your answers to two decimal places) for the two samples.

290.0 458.8

5517.41 18933.32

18933.32 137.6

What does this information tell you about the prices for flights into these two cities?

The prices for round-trip flights into Atlanta are less variable than prices for round-trip flights into Salt Lake City.

21. The Los Angeles 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: , , , , , , , , and .

a. Compute the range and interquartile range.

b. Compute the sample variance and sample standard deviation (to decimals).

92.75

9.63

c. A sample of air quality index readings for Anaheim provided a sample mean of , a sample variance of , and a sample standard deviation of . What comparisons can you make between the air quality in Pomona and that in Anaheim on the basis of these descriptive statistics?

The air quality variability is greater in Anaheim.

22. According to the Consumer Expenditure Survey, Americans spend an average of on cellular phone service annually (U.S. Bureau of Labor Statistics website). Suppose that we wish to determine if there are differences in cellular phone expenditures by age group. Therefore, samples of consumers were selected for three age groups (, , and older). The annual expenditure for each person in the sample is provided in the table below.

a. Compute the mean, variance, and standard deviation for each of these three samples. Round your answers to one decimal place.

1368 1330.1 1070.4

292467.3 186332.32 111866.04

540.80 540.80 334.4638

b. What observations can be made based on these data?

45 and older

18 – 34

23. Scores turned in by an amateur golfer at the Bonita Fairways Golf Course in Bonita Springs, Florida, during and are as follows:

2018 Season:		75	79	80	78	76	74	76	78
2019 Season:		72	71	76	78	86	81	72	80

a. Use the mean (to the nearest whole number) and standard deviation (to decimals) to evaluate the golfer’s performance over the two-year period.

2.07

5.26

b. What is the primary difference in performance between and ?

The variation in scores was higher in 2019.

What improvement, if any, can be seen in the scores?

In 2019, three of the eight scores were better (lower) than the best score of 2018.

24. Consider a sample with data values of , , , , and . Compute the -score for each of the five observations (to decimals). Enter negative values as negative numbers.

-1.25

1.25

-0.75

0.5

0.25

25. The Graduate Management Admission Test (GMAT) is a standardized exam used by many universities as part of the assessment for admission to graduate study in business. The average GMAT score is (Magoosh website). Assume that GMAT scores are bell-shaped with a standard deviation of . Use the empirical rule to answer the following.

a. What percentage of GMAT scores are or higher (to decimal)?

b. What percentage of GMAT scores are or higher (to decimal)?

2.5

c. What percentage of GMAT scores are between and (to decimal)?

d. What percentage of GMAT scores are between and (to decimal)?

81.5

26. Each year Money magazine publishes a list of “Best Places to Live in the United States.” These listings are based on affordability, educational performance, convenience, safety, and livability. The below table shows the median household income of Money magazine’s top city in each U.S. state for (Money magazine website).

a. Compute the mean and median for these household income data.

72342.94

66743

b. Compare the mean and median values for these data. What does this indicate about the distribution of household income data?

larger

positively

c. Compute the range and standard deviation for these household income data.

100132

23711.80

d. Compute the first and third quartiles for these household income data.

56562.75

82775.75

e. How many values would be considered outliers are in these data? If an amount is zero, enter “0”.

What does this suggest about the data?

Since there are outliers above the upper limit of the data, this is most likely why the mean is larger than the median.

27. The New York Times reported that Apple has unveiled a new iPad marketed specifically to school districts for use by students (The New York Times website). The -inch iPads will have faster processors and a cheaper price point in an effort to take market share away from Google Chromebooks in public school districts. Suppose that the following data represent the percentages of students currently using Apple iPads for a sample of U.S. public school districts.

a. Compute the mean and median percentage of students currently using Apple iPads.

24.67

b. Compute the first and third quartiles for these data.

26.25

c. Compute the range and interquartile range for these data.

8.25

d. Compute the variance and standard deviation for these data.

140.82

11.87

e. Are there any outliers in these data? Enter the number of outliers. If an amount is zero, enter “0”.

f. Based on your calculated values, what can we say about the percentage of students using iPads in public school districts?

Relative to the mean. there are some school districts where many more students are using iPads.

28. Consider a sample with data values of , , , , , , , and .

Which boxplot most accurately represents these data?

boxplot #2

29. Fortune magazine’s list of the world’s most admired companies for is provided in the data contained in the file AdmiredCompanies (Fortune magazine website). The data in the column labeled “Return” shows the one-year total return () for the top-ranked companies. For the same time period the S&P average return was .

a. Compute the median return for the top-ranked companies (to decimal).

13.9

b. What percentage of the top-ranked companies had a one-year return greater than the S&P average return (to the nearest percent)?

c. Develop the five-number summary for the data. If required, round your answers to two decimals places. If required, enter negative values as negative numbers.

-13.9

3.7

13.9

117.1

d. Are there any outliers?

Yes

e. Select a boxplot for the one-year total return.

Boxplot 1

30. A random sample of colleges from Kiplinger’s list of the best values in private college provided the data shown in the file BestPrivateColleges (Kiplinger website). The variable Admit Rate () shows the percentage of students that applied to the college and were admitted, and the variable -yr Grad. Rate () shows the percentage of students that were admitted and graduated in four years.

a. Select a scatter diagram with Admit Rate () as the independent variable.

Scatter diagram 1

What does the scatter diagram indicate about the relationship between the two variables?

Negative linear relationship

b. Compute the sample correlation coefficient. Round your answer to two decimal places and enter negative value as negative number, if necessary.

-0.76

What does the value of the sample correlation coefficient indicate about the relationship between the Admit Rate () and the -yr Grad. Rate ()?

Negative Linear relationship

31. Public transportation and the automobile are two methods an employee can use to get to work each day. Samples of travel times recorded for each method are shown. Times are in minutes.

a. Compute the sample mean time to get to work for each method (to the nearest whole number).

b. Compute the sample standard deviation for each method (to decimals).

4.64

1.83

c. On the basis of your results from parts (a) and (b), which method of transportation should be preferred? Explain.

Automobile, because the variability is lower.

Does a comparison of the boxplots support your conclusion in part (c)?

Yes, the boxplots support the conclusion by showing the difference in variation between both methods of transportation.

31. 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. Round your answer to decimal places.

9.75

32. A study on driving speed (miles per hour) and fuel efficiency (miles per gallon) for midsize automobiles resulted in the following data:

a. Which of the following is a scatter diagram with driving speed on the horizontal axis and fuel efficiency on the vertical axis?

b. Comment on any apparent relationship between these two variables.

Higher

33. The Northwest regional manager of an outdoor equipment retailer conducted a study to determine how managers at three store locations are using their time. A summary of the results are shown in the following table. Click on the datafile logo to reference the data.

a. Which of the following shows a correct stacked bar chart with store location on the horizontal axis and percentage of time spent on each task on the vertical axis?

b. Which of the following shows a correct side-by-side bar chart with store location on the horizontal axis and side-by-side bars of the percentage of time spent on each task?

c. Which type of bar chart (stacked or side-by-side) do you prefer for these data? Why?

stacked

34. Consider the following frequency distribution.

Class	Frequency
10 – 19	10
20 – 29	14
30 – 39	17
40 – 49	7
50 – 59	2

Which of the following histograms accurately represents the data?

Histogram #3

35. Consider the following data on two categorical variables. The first variable, , can take on values , , , or . The second variable, , can take on values or.

The following table gives the frequency with which each combination occurs.

a. Select a correct side-by-side bar chart with on the horizontal axis.