How large a sample of the hotel mangers in Exercise 6.27 would be needed to estimate the mean m within +/- 1 year with 99% confidence?

| June 8, 2016

1) 6.30 Hotel managers. p.350
How large a sample of the hotel mangers in Exercise 6.27 would be needed to estimate the mean m within +/- 1 year with 99% confidence?

(Ex: 6.27 In a study of the career paths of hotel general managers, questionnaires were sent to an SRS of 160 hotels belonging to major U.S. hotel chains. There were 114 responses. The average time these 114 GMs had spent with their current company was11.8 years. Give a 99% confidence interval for the mean number of years general managers of major-chain hotels have spent with their current company. – Take it as known that the standard deviation of time with the company for all general managers is 3.2 years)

2)6.66 Financial aid. p.369
The financial aid office of a university asks a sample of students about their employment and earnings. The report says that “for academic year earnings, a significant difference (P=0.038) was found between the sexes, with men earning more on the average. No difference (P=0.476) was found between the earnings of black and white students.” Explain both of these conclusions, for the effects of sex and of race on mean earnings, in language understandable to someone who knows no statistics.

3)6.78 Clothing for runners p.370
Your company sells exercise clothing and equipment on the internet. To design the clothing you collect data on the physical characteristics of your different types of customers. Here are the weights for a sample of 24 male runners. Assume that these runners can be viewed as a random sample of your potential customers. The weights are expressed in kilograms.

68.7 61.8 63.2 53.1 62.3 59.7 55.4 58.9 60.9 69.2 63.7 67.8
65.6 65.5 56.0 57.8 66.0 62.9 53.6 65.0 55.8 60.4 69.3 62.1

7.44 Potential insurance fraud? p.416 (Hint: define μ as the difference between the two garages, and then test μ=0 or not.)

Insurance adjusters are concerned about the high estimates they are receiving for Jocko’s Garage. TO see if the estimates are unreasonably high, each of 10 damaged cars was taken to Jocko’s and to a “trusted” garage and the estimates recorded. Here are the results:

Car: 1 2 3 4 5
Jocko’s 50 1550 1250 1300 750
Other 430 1500 1300 1280 780
Car 6 7 8 9 10
Jocko’s 1000 1210 1300 800 2500
Other 870 1120 1140 650 2290

7.114 Number of critical food violations. p.447

The results of a major city’s restaurant inspections are available through its online newspaper. Critical food violations are those that put patrons at risk of getting sick and must be immediately corrected by the restaurant. An SRS of n = 200 inspections from the more than 4400 inspections since January 2008 had = 1.20 violations and s = 1.81 violations.

a) Test the hypothesis, usingα= 0.05, that the average number of critical violations is less than 1.5. State the two hypotheses, the test statistic and P-value.

b) Construct a 95% confidence interval for the average number of critical violations and summarize your result.

c) Which of the two summaries (significance test versus confidence interval) do you find more helpful in this case? Explain your answer.

d) These data are integers ranging from 0-9. The data are also skewed to the right, with 70% of the values either a 0 or 1. Given this information, do you feel use of the t procedures is appropriate? Explain your answer.

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