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

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

a. Compare the mean drop in blood pressure for the high-dose group and the control

group. Use a ⫽ .05 and report the level of significance.

b. Estimate the size of the difference in the mean drop for the high-dose and control

groups using a 95 confidence interval.

c. Do the conditions required for the statistical techniques used in a and b appear to

be satisfied? Justify your answer. 6.51 Refer to Exercise 6.50. a. Compare the mean drop in blood pressure for the low-dose group and the control group. Use a ⫽ .05 and report the level of significance.

b. Estimate the size of the difference in the mean drop for the low-dose and control

groups using a 95 confidence interval.

c. Do the conditions required for the statistical techniques used in a and b appear to

be satisfied? Justify your answer. 6.52 Refer to Exercise 6.50. a. Compare the mean drop in blood pressure for the low-dose group and the high-dose group. Use a ⫽ .05 and report the level of significance.

b. Estimate the size of the difference in the mean drop for the low-dose and high-dose

groups using a 95 confidence interval.

c. Do the conditions required for the statistical techniques used in a and b appear to

be satisfied? Justify your answer. 6.53 In Exercises 6.50 – 6.52, we tested three sets of hypotheses using portions of the same data sets in each of the sets of hypotheses. Let the experiment-wide Type I error rate be defined as the probability of making at least one Type I error in testing any set of hypotheses using the data from the experiment.

a. If we tested each of the three sets of hypotheses at the .05 level, estimate the experiment-

wide Type I error rate.

b. Suggest a procedure by which we could be ensured that the experiment-wide Type I

error rate would be at most .05. Two-sample T for Low Dose vs Control N Mean StDev SE Mean Low Dose 20 3.8 44.0 9.8 Control 20 29.8 34.0 7.6 95 CI for mu Low Dose mu Control: 51.3, 0.8 T-Test mu Low Dose mu Control vs not : T 2.09 P 0.044 DF 35 -------------------------------------------------------------------------------- Two-sample T for High Dose vs Control N Mean StDev SE Mean High Dose 20 68.4 24.5 5.5 Control 20 29.8 34.0 7.6 95 CI for mu High Dose mu Control: 19.5, 57.6 T-Test mu High Dose mu Control vs not : T 4.12 P 0.0002 DF 34 -------------------------------------------------------------------------------- Two-sample T for Low Dose vs High Dose N Mean StDev SE Mean Low Dose 20 3.8 44.0 9.8 High Dose 20 68.4 24.5 5.5 95 CI for mu Low Dose mu High Dose: 87.6, 41.5 T-Test mu Low Dose mu High Dose vs not : T 5.73 P 0.0000 DF 29