Is there significant evidence that on a typical day the mine produces more than

a. Estimate the average amount of SO

2 emissions during each of the three time periods using 95 confidence intervals.

b. Does there appear to be a significant difference in average SO

2 emissions over the three time periods?

c. Combining the data over the entire day, is the average SO

2 emissions using the new scrubber less than .145, the average daily value for the old scrubber? Soc. 5.72 As part of an overall evaluation of training methods, an experiment was conducted to de- termine the average exercise capacity of healthy male army inductees. To do this, each male in a random sample of 35 healthy army inductees exercised on a bicycle ergometer a device for measuring work done by the muscles under a fixed work load until he tired. Blood pressure, pulse rates, and other indicators were carefully monitored to ensure that no one’s health was in danger. The exercise capacities mean time, in minutes for the 35 inductees are listed here. 23 19 36 12 41 43

19 28

14 44 15 46 36 25 35 25 29 17 51 33 47 42 45 23 29 18 14 48 21 49

27 39

44 18 13

a. Use these data to construct a 95 confidence interval for m, the average exercise

capacity for healthy male inductees. Interpret your findings. b. How would your interval change using a 99 confidence interval? 5.73 Using the data in Exercise 5.72, determine the number of sample observations that would be required to estimate m to within 1 minute, using a 95 confidence interval. Hint: Substitute s ⫽ 12.36 for s in your calculations. H.R. 5.74 Faculty members in a state university system who resign within 10 years of initial em- ployment are entitled to receive the money paid into a retirement system, plus 4 per year. Un- fortunately, experience has shown that the state is extremely slow in returning this money. Concerned about such a practice, a local teachers’ organization decides to investigate. From a random sample of 50 employees who resigned from the state university system over the past 5 years, the average time between the termination date and reimbursement was 75 days, with a standard deviation of 15 days. Use the data to estimate the mean time to reimbursement, using a 95 confidence interval. 5.75 Refer to Exercise 5.74. After a confrontation with the teachers’ union, the state promised to make reimbursements within 60 days. Monitoring of the next 40 resignations yields an aver- age of 58 days, with a standard deviation of 10 days. If we assume that these 40 resignations rep- resent a random sample of the state’s future performance, estimate the mean reimbursement time, using a 99 confidence interval. Bus. 5.76 Improperly filled orders are a costly problem for mail-order houses. To estimate the mean loss per incorrectly filled order, a large firm plans to sample n incorrectly filled orders and to determine the added cost associated with each one. The firm estimates that the added cost is between 40 and 400. How many incorrectly filled orders must be sampled to estimate the mean additional cost using a 95 confidence interval of width 20? Eng. 5.77 The recipe for producing a high-quality cement specifies that the required percentage of SiO 2 is 6.2. A quality control engineer evaluates this specification weekly by randomly selecting samples from n ⫽ 20 batches on a daily basis. On a given day, she obtained the following values: 1.70 9.86 5.44 4.28 4.59 8.76 9.16 6.28 3.83 3.17 5.98 2.77 3.59 3.17 8.46 7.76 5.55 5.95 9.56 3.58

a. Estimate the mean percentage of SiO

2 using a 95 confidence interval.

b. Evaluate whether the percentage of SiO

2 is different from the value specified in the recipe using an a ⫽ .05 test of hypothesis.

c. Use the following plot to determine if the procedures you used in parts a and b

were valid.

5.78 Refer to Exercise 5.77. a. Estimate the median percentage of SiO

2 using a 95 confidence interval.

b. Evaluate whether the median percentage of SiO

2 is different from 6.2 using an a ⫽ .05 test of hypothesis.

5.79 Refer to Exercise 5.77. Generate 1,000 bootstrap samples from the 20 SiO

2 percentages.

a. Construct a 95 bootstrap confidence interval on the mean SiO

2 percentage. Compare this interval to the interval obtained in Exercise 5.77a.

b. Obtain the bootstrap p-value for testing whether the mean percentage of SiO

2 differs from 6.2. Compare this value to the p-value for the test in Exercise 5.77b.

c. Why is there such a good agreement between the t-based and bootstrap values in

parts a and b? Med. 5.80 A medical team wants to evaluate the effectiveness of a new drug that has been proposed for people with high intraocular pressure IOP. Prior to running a full-scale clinical trial of the drug, a pilot test was run using 10 patients with high IOP values. The n ⫽ 10 patients had a mean decrease in IOP of ⫽ 15.2 mm Hg with a standard deviation of the 10 IOPs equal to s ⫽ 9.8 mm Hg after 15 weeks of using the drug. Determine the appropriate sample size for an a ⫽ .01 test to have at most a .10 probability of a failing to detect at least a 4 mm Hg decrease in the mean IOP. y 2 4 6 8 10 12 SiO 2 Evaluation of normality 5 1

10 20

Percent 30 40 50 60 70 80 90 95 99 P -Value 0.100 RJ 0.975 N 20 StDev 2.503 Mean 5.673