# Statistics

8.3

Why is it not possible in Example 8.1 on page 256 to have 100% confidence? Explain.

8.19

The file Sedans contains the overall miles per gallon (MPG) of 2009 sedans priced under \$20.000.

27 31 30 28 27 24 29 32 32 27 26 26 25 26 25 24

Source: Data extracted from “Vehicle Ratings,” Consumer Reports, April 2009, p. 27

a) Construct a 95% confidence interval estimate for the population mean MPG of 2009 sedans (4 cylinder) priced under \$20.000, assuming a normal distribution.

b) Interpret the interval constructed in (a).

c) Compare the results in (a) to those in Problem 8.20 (a)

8.22

One of the major measures of the quality of service provided by any organization is the speed with which t responds to customer complaints. A large family-held department store selling furniture and flooring, including carpet, had undergone a major expansion in the past several years. In particular, the flooring department had expanded from 2 installation crews. The store had the business objective of improving its response to complaints. The variable of interest was defined as the number of days between when the complaint was made and when it was resolved. Data were collected from 50 complaints that were made in the last year. The data were stored in Furniture and are as follows:

54

5

35

137

31

27

152

2

123

81

74

27

11

19

126

110

110

29

61

35

94

31

26

5

12

4

165

32

29

28

29

26

25

1

14

13

13

10

5

27

4

52

30

22

36

26

20

23

33

68

a) Construct a 95% confidence interval estimate for the population mean number of days between the receipt of a complaint and the resolution of the complaint.

b) What assumption must you make about the population distrubiton in order to construct the confidence interval estimate in (a)?

c) Do you think that the assumption needed in order to construct the confidence interval estimate in (a) is valid? Explain

d) What effect might your conclusion in (c) have on the validity of the results in (a)?

8.23

In New York State, savings banks are permitted to sell a form of life insurance called savings bank life insurance (SBLI). The approval process consists of underwriting, which includes a review of the application a medical information bureau check, possible requests for additional medical information and medical exams, and a policy compilation stage in which the policy pages are generated and sent tot the bank for delivery. The ability to deliver approved policies to customers in a timely manner is critical to the profitability of this service to the bank. During a period of one month, a random sample of 27 approved policies was selected, and the total processing time, in days, was a s shown below and stored in Insurance:

73

19

16

64

28

28

31

90

60

56

31

56

22

18

45

48

17

17

17

91

92

63

50

51

69

16

17

a) Construct a 95% confidence interval estimate for the population mean processing time.
b) What assumption must you make about the population distribution order to construct the confidence interval estimate in (a)?
c) Do you think that the assumption needed in order to construct the confidence interval estimate in (a) is valid? Explain.