Review for Ch. 1, 2

1. Parking at a large university has become a very big problem. University administrators are interested in determining the average parking time (e.g. the time it takes a student to find a parking spot) of it's students. An administrator inconspicuously followed 250 students and carefully recorded their parking times. Identify the population of interest to the university administration.

a. The 250 students that data was collected from.

b. The entire set of students that park at the university.

c. The entire set of faculty, staff, and students that park at the university.

d. The students that park at the university between 9 and 10 AM on Wednesdays.

 

2. The amount of television viewed by today's youth is of primary concern to Parents Against Watching Television (PAWT). 300 parents of elementary school-aged children were asked to estimate the number of hours per week that their child watched television. The mean and the standard deviation for their responses were 15 and 5, respectively. Identify the type of data collected by PAWT.

a. Quantitative

b. Qualitative

 

3. A published report recently stated "Based on a sample of 150 new cars, there is evidence to indicate that the average new car price of all foreign automobiles is significantly higher than the average new car price of all American cars." This statement is an example of a(n) ___________.

a. random sample

b. statistical inference

c. population

d. descriptive statistic

 

4. A personnel director at a large company studied the eating habits of the company's employees. The director noted whether an employee brought their own lunch to work, ate at the company cafeteria, or went out to eat lunch. The goal of the study was to improve the company cafeteria. This type of data collection would best be considered as a(n) __________.

a. observational study

b. designed experiment

c. random sample

d. survey sample

 

5. The U.S. Open Championship was just played in New York and Pete Sampras was, again, one of the men's best players. The U.S. Open statistician kept track of every serve that Pete Sampras hit during the tennis tournament. The statistician reported that the mean serve speed was 100 miles per hour (mph) and the standard deviation of the serve speeds was 15 mph. If nothing is known about the shape of the distribution, give an interval of speeds that will contain the speeds of at least 8/9th's of Pete Sampras' serves.

a. 85 mph to 115 mph

b. 70 mph to 130 mph

c. 55 mph to 145 mph

d. 100 mph to 160 mph

 


 

6. The amount of television viewed by today's youth is of primary concern to Parents Against Watching Television (PAWT). 300 parents of elementary school-aged children were asked to estimate the number of hours per week that their child watched television. The mean and the standard deviation for their responses were 15 and 5, respectively. PAWT constructed a stem-and-leaf display for the data that showed that the distribution of times was a symmetric mound-shaped distribution. Give an interval where you believe most (approximately 95%) of the television viewing times fell in the distribution.

a. between 10 and 20 hours per week

b. between 5 and 25 hours per week

c. between 0 and 20 hours per week

d. less than 15 hours per week

 

7. The 1995 payroll amounts for all major-league baseball teams are shown below using a graphical technique from chapter 2 of the text. Answer the following questions concerning this graph. What proportion of the payrolls were in the $10-$20 million range?

a. 2

b. .0714

c. .0769

d. .0667

 


 

8. A survey was conducted to determine how people rated the quality of programming available on television. Respondents were asked to rate the overall quality from 0 (no quality at all) to 100 (extremely good quality). The stem-and-leaf display of the data is shown below.

 

Stem Leaves

3 2 4

4 0 3 4 7 8 9 9 9

5 0 1 1 2 3 4 5

6 1 2 5 6 6

7 0 1

8

9 2

 

What percentage of the respondents rated overall television quality as very good (regarded as ratings of 80 and above)?

a. .04

b. 1

c. .96

d. 0

 

9. A sample of fifty motorists was taken on a Federal highway where the speed limit was 55 miles per hour. A dot plot of their speeds is shown below.

 

What proportion of the motorists were speeding?

a. .50

b. 4

c. . 08

d. 25

 

Health care issues are receiving much attention in both academic and political arenas. A sociologist recently conducted a survey of citizens over 60 years of age whose net worth is too high to qualify for Medicaid but who have no private health insurance. The ages of 25 uninsured senior citizens were as follows:

 

68 73 66 76 86 74 61 89 65 90 69 92 76

62 81 63 68 81 70 73 60 87 75 64 82

 

10. Find the median of the observations.

a. 70

b. 73

c. 74

d. 73.5

 


 

11. Suppose the mean and standard deviation are 74.04 and 9.75, respectively. If we assume that the distribution of ages is mound-shaped and symmetric, what percentage of the respondents will be between 64.29 and 93.54 years old?

a. Approximately 81.5%

b. Approximately 68%

c. Approximately 95%

d. Approximately 84%

 

Each year advertisers spend billions of dollars purchasing commercial time on network sports television. In the first 6 months of 1988, advertisers spent $1.1 billion. Who were the largest spenders? In a recent article, Real and Mechikoff (1992) list the top 10 leading spenders (in million of dollars):

 

Chrysler $72.0 AT&T $26.9

General Motors 63.1 Sears 25.0

Philip Morris 54.7 U.S. Armed Forces 23.9

Anheuser-Busch 54.3 McDonald's 23.0

Ford 29.0 American Express 20.0

 

12. Calculate the sample variance.

a. 19.5433

b. 381.939

c. 18.5404

d. 343.745

 

13. Assuming that the mean and standard deviation are 40 and 19, respectively, calculate the z-score for the Chrysler expenditure.

a. 32

b. .594

c. 1.68

d. .292

 

14. The distribution of salaries of professional basketball players is skewed to the right. Which measure of central tendency would be the best measure to determine the location of the center of the distribution?

a. Median

b. Mode

c. Mean

d. Range

 


 

15. For the distribution drawn here, identify the mean, median, and mode.

a. A = median, B = mode, C = mean

b. A = mode, B = mean, C = median

c. A = mode, B = median, C = mean

d. A = mean, B = mode, C = median

 

16. For the following group of data, calculate the range:

 

6, 3, 7, 2, 5, 10, 8, 7, 8

a. 6

b. 9

c. 7

d. 8

 

17. Last year batting averages in the National League averaged 0.264 with a

high of .337 and a low of .216(minimum 250 at-bats). Based on this information, which measure of variation could be calculated?

a. variance

b. range

c. standard deviation

d. percentile

 

18. The book cost (in dollars) for one semester's books are given below for a sample of five college students. Calculate the variance of the book costs.

 

200, 250, 375, 125, 280

 

a. 92.965

b. 8642.5

c. 83.1505

d. 6914.0

 


19. The bar graph below shows the political party affiliation of 1,000 registered U.S. voters. What percentage of the 1,000 registered U.S. voters belonged to one of the traditional two parties (Democratic and Republican)?

a. .40

b. .75

c. .35

d. .25

 

20. Fill in the blank. One advantage of the ____________ is that the actual data values are retained in the graphical summarization of the data.

a. bar graph

b. box plot

c. stem-and-leaf plot

d. pie chart

 

21. Fill in the blank. ____________ gives us a method of interpreting the standard deviation that applies to any data set, regardless of the shape of the distribution.

a. Chebyshev's rule

b. The Empirical Rule

c. Both a and b

d. Neither a nor b

 

22. To what type of data can Chebyshev's rule be applied?

a. Skewed left data

b. Symmetric data

c. Skewed right data

d. All of the above

 


 

23. The amount of television viewed by today's youth is of primary concern to Parents Against Watching Television (PAWT). 300 parents of elementary school-aged children were asked to estimate the number of hours per week that their child watched television. The upper quartile for the distribution was given as 17 hours. Interpret this value.

 

24. Each year advertisers spend billions of dollars purchasing commercial time on network sports television. In the first 6 months of 1988, advertisers spent $1.1 billion. Who were the largest spenders? In a recent article, Real and Mechikoff (1992) list the top 10 leading spenders (in million of dollars):

 

Chrysler $72.0 AT&T $26.9

General Motors 63.1 Sears 25.0

Philip Morris 54.7 U.S. Armed Forces 23.9

Anheuser-Busch 54.3 McDonald's 23.0

Ford 29.0 American Express 20.0

 

Calculate the mean and median for the data.

 

25. The scores for a statistics test are as follows:

 

87 76 96 77 94 92 88 85 66 89

79 95 50 91 83 88 82 58 18 69

 

Create a stem-and-leaf display for the data.

 

26. By law, a box of cereal labeled as containing 16 ounces must contain at least 16 ounces of cereal. It is known that the machine filling the boxes produces a distribution of fill weights that is mound-shaped, with mean equal to the setting on the machine and with a standard deviation equal to 0.03 ounce. To ensure that most of the boxes contain at least 16 ounces, the machine is set so that the mean fill per box is 16.09 ounces. What percentage of the boxes do, in fact, contain at least 16 ounces?

 

27. A study was designed to investigate the effects of two variables(1) a student's level of mathematical anxiety and (2) teaching method on a student's achievement in a course in mathematics. Students who had a low level of mathematical anxiety were taught using the traditional expository method. These students obtained a mean score of 180 and a standard deviation of 50 on a standardized test. Find the z-score of a student who scored 250 on the standardized test.

 


 

Answers

 

1. b

2. a

3. b

4. a

5. c

6. b

7. c

8. a

9. a

10. b

11. a

12. b

13. c

14. a

15. c

16. d

17. b

18. b

19. b

20. c

21. a

22. d

23. 75% of the TV viewing times will be less than 17 hours per week. 25% of the TV times will exceed 17 hours per week.

24. _

The mean of the data is x =

72.0 + 63.1 + 54.7 + 54.3 + 29.0 + 26.9 + 25.0 + 23.9 + 23.0 + 20.0 =

10

391.9

= 10

= $39.1 million

 

The median is the average of the middle two observations.

 

29.0 + 26.9

 

M = $27.95 million

 

25. The stem will consist of the tens digit and range from 1 to 9. The

leaves will be drawn in the appropriate stems based on the data

values.

 

Stem Leaves

1 8

2

3

4

5 0 8

6 6 9

7 6 7 9

8 7 8 5 9 3 8 2

9 6 4 2 5 1

26. The value of 16 ounces falls three standard deviations below the mean. The Empirical Rule states that approximately all of the boxes will contain cereal amounts between 16.00 ( - 3σ) and 16.18 (μ + 3σ). Therefore, approximately 100% of the boxes contain at least 16 ounces. (More accurate 99.85%)


 

27.

 

250 180 = 1.4

For a score of 250, z = 50

 

This student's score falls 1.4 standard deviations above the mean

score of 180.

 

28. Mean = 58.24: The arithmetic average of the 25 tree heights is 58.24 inches.

Median = 58.00: Half of the sampled tree heights exceeded 58 inches.