An entomologist is investigating which of two fumigants, F

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. 6.48 Refer to Exercise 6.46. The researchers also examined the effect of depth on population abundance.

a. Plot the four data sets using side-by-side boxplots to demonstrate the effect of depth

on population abundance.

b. Separately for each depth, evaluate differences between the sites within and outside

the oil trajectory. Use a = .05. c. Are your conclusions at 40 m consistent with your conclusions at 100 m? 6.49 Refer to Exercises 6.46 – 6.48.

a. Discuss the veracity of the following statement: “The oil spill did not adversely affect the

population abundance; in fact, it appears to have increased the population abundance.”

b. A possible criticism of the study is that the six sites outside the oil trajectory were not

comparable in many aspects to the seven sites within the oil trajectory. Suppose that the researchers had data on population abundance at the seven within sites prior to the oil spill. What type of analysis could be used on these data to evaluate the effect of the oil spill on population abundance? What are some advantages to using these data rather than the data in Exercise 6.46?

c. What are some possible problems with using the before and after oil spill data in

assessing the effect of the spill on population abundance? Bio. 6.50 A study was conducted to evaluate the effectiveness of an antihypertensive product. Three groups of 20 rats each were randomly selected from a strain of hypertensive rats. The 20 rats in the first group were treated with a low dose of an antihypertensive product, the second group with a higher dose of the same product, and the third group with an inert control. Note that negative values represent increases in blood pressure. The accompanying computer output can be used to answer the following questions. Row Low Dose High Dose Control 1 45.1 54.2 18.2 2 59.8 89.1 17.2 3 58.1 89.6 34.8 4 23.7 98.8 3.2 5 64.9 107.3 42.9 6 12.1 65.1 27.2 7 10.5 75.6 42.6 8 42.5 52.0 10.0 9 48.5 50.2 102.3 10 1.7 80.9 61.0 11 65.4 92.6 33.1 12 17.5 55.3 55.1 13 22.1 103.2 84.6 14 15.4 45.4 40.3 15 96.5 70.9 30.5 16 27.7 29.7 18.5 17 16.7 40.3 29.3 18 39.5 73.3 19.7 19 4.2 21.0 37.2 20 41.3 73.2 48.8 ------------------------------------------- 100 50 –50 Low-dose group High-dose group 1 2 3 Control group Blood pressure Boxplot of blood pressure data