Suppose the sample sizes are the same for both groups. What sample size is needed

The amount of pollution in ppm detected from the cooling towers before and after the scrub- bers were installed is given below for 23 chemical plants. Mean Standard Deviation Before Scrubber 71 26 After Scrubber 63 25 Difference ⫽ Before ⫺ After 8 20 Suppose a larger study is planned for a state with a more extreme pollution problem.

a. How many chemical plant cooling towers need to be measured if we want a probabil-

ity of .90 of detecting a mean reduction in pollution of 10 ppm due to installing the scrubber using an a ⫽ .01 test? b. What assumptions did you make in part a in order to compute the sample size? Env. 6.41 Refer to Exercise 6.40. The state regulators also need to obtain precise estimates of the mean reduction in the pollution levels after installing the scrubber. What sample size is needed to obtain a 95 confidence interval for the mean reduction using a 99 confidence interval having width of 10 ppm? Supplementary Exercises Med. 6.42 Long-distance runners have contended that moderate exposure to ozone increases lung capacity. To investigate this possibility, a researcher exposed 12 rats to ozone at the rate of 2 parts per million for a period of 30 days. The lung capacity of the rats was determined at the beginning of the study and again after the 30 days of ozone exposure. The lung capacities in mL are given here. Rat 1 2 3 4 5 6 7 8 9 10 11 12 Before exposure 8.7 7.9 8.3 8.4 9.2 9.1 8.2 8.1 8.9 8.2 8.9 7.5 After exposure 9.4 9.8 9.9 10.3 8.9 8.8 9.8 8.2 9.4 9.9 12.2 9.3

a. Is there sufficient evidence to support the conjecture that ozone exposure increases

lung capacity? Use a ⫽ .05. Report the p-value of your test.

b. Estimate the size of the increase in lung capacity after exposure to ozone using a 95

confidence interval.

c. After completion of the study, the researcher claimed that ozone causes increased

lung capacity. Is this statement supported by this experiment? Env. 6.43 In an environmental impact study for a new airport, the noise level of various jets was measured just seconds after their wheels left the ground. The jets were either wide-bodied or narrow-bodied. The noise levels in decibels dB are recorded here for 15 wide-bodied jets and 12 narrow-bodied jets. Wide-Bodied Jet 109.5 107.3 105.0 117.3 105.4 113.7 121.7 109.2 108.1 106.4 104.6 110.5 110.9 111.0 112.4 Narrow-Bodied Jet 131.4 126.8 114.1 126.9 108.2 122.0 106.9 116.3 115.5 111.6 124.5 116.2 a. Do the two types of jets have different mean noise levels? Report the level of significance of the test.

b. Estimate the size of the difference in mean noise level between the two types of jets

using a 95 confidence interval. c. How would you select the jets for inclusion in this study? Ag.

6.44 An entomologist is investigating which of two fumigants, F

1 or F 2 , is more effective in controlling parasities in tobacco plants. To compare the fumigants, nine fields of differing soil