Suppose the user group will have twice as many patients as the placebo group. What

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 characteristics, drainage, and amount of wind shield were planted with tobacco. Each field was then divided into two plots of equal area. Fumigant F 1 was randomly assigned to one plot in each field and F 2 to the other plot. Fifty plants were randomly selected from each field, 25 from each plot, and the number of parasites were counted. The data are in the following table. Field 1 2 3 4 5 6 7 8 9 Fumigant F 1 77 40 11 31 28 50 53 26 33 Fumigant F 2 76 38

10 29

27 48 51 24

32

a. What are the populations of interest? b. Do the data provide sufficient evidence to indicate a difference in the mean level of parasites for the two fumigants? Use a ⫽ .10. Report the p-value for the experimental data.

c. Estimate the size of the difference in the mean number of parasites between the two

fumigants using a 90 confidence interval. 6.45 Refer to Exercise 6.44. An alternative design of the experiment would involve ran- domly assigning fumigant F 1 to nine of the plots and F 2 to the other nine plots, ignoring which fields the plots were from. What are some of the problems that may occur in using the alternative design? Env. 6.46 Following the March 24, 1989, grounding of the tanker Exxon Valdez in Alaska, ap- proximately 35,500 tons of crude oil were released into Prince William Sound. The paper “The deep benthos of Prince William Sound, Alaska, 16 months after the Exxon Valdez oil spill” [Marine Pollution Bulletin 1998, 36:118 –130] reports on an evaluation of deep benthic in- fauna after the spill. Thirteen sites were selected for study. Seven of the sites were within the oil trajectory and six were outside the oil trajectory. Collection of environmental and biological data at two depths, 40 m and 100 m, occurred in the period July 1–23, 1990. One of the variables measured was population abundance individuals per square meter. The values are given in the following table. Within Oil Trajectory Outside Oil Trajectory Site 1 2 3 4 5 6 7 1 2 3 4 5 6 Depth 40 m 5,124 2,904 3,600 2,880 2,578 4,146 1,048 1,336 394 7,370 6,762 744 1,874 Depth 100 m 3,228 2,032 3,256 3,816 2,438 4,897 1,346 1,676 2,008 2,224 1,234 1,598 2,182

a. After combining the data from the two depths, does there appear to be a difference in

population mean abundance between the sites within and outside the oil trajectory? Use a ⫽ .05.

b. Estimate the size of the difference in the mean population abundance at the two

types of sites using a 95 confidence interval. c. What are the required conditions for the techniques used in parts a and b? d. Check to see whether the required conditions are satisfied.

6.47 Refer to Exercise 6.46. Answer the following questions using the combined data for both depths.

a. Use the Wilcoxon rank sum test to assess whether there is a difference in population

abundance between the sites within and outside the oil trajectory. Use a ⫽ .05. b. What are the required conditions for the techniques used in part a? c. Are the required conditions satisfied?

d. Discuss any differences in the conclusions obtained using the t-procedures and the

Wilcoxon rank sum test.