What has a greater effect, if any, on the level of significance of the Wilcoxon rank sum

6.21 Refer to Exercises 6.19 and 6.20. a. For what type of population distributions would you recommend using the t test? Justify your answer.

b. For what type of population distributions would you recommend using the Wilcoxon

rank sum test? Justify your answer. 6.4 Inferences about M 1 ⴚ M 2 : Paired Data 6.22 Set up the rejection regions for testing the following:

a. H

: m d ⫽ 0 versus H a : m d ⫽ 0, with n 1 ⫽ 11, n 2 ⫽ 14, and a ⫽ .05

b. H

: m d ⱕ 0 versus H a : m d ⬎ 0, with n 1 ⫽ n 2 ⫽ 17, and a ⫽ .01

c. H

: m d ⱖ 0 versus H a : m d ⬍ 0, with n 1 ⫽ 8, n 2 ⫽ 12, and a ⫽ .025

6.23 Consider the data given here. Pair

1 2 3 4 5 6 y 1 48.2 44.6 49.7 40.5 54.6 47.1 y 1 41.5 40.1 44.0 41.2 49.8 41.7

a. Conduct a paired t test of H

: m d ⱕ 0 versus H a : m d ⬎ 0 with d ⫽ y 1 ⫺ y 2 . Use a ⫽ .05

b. Using a testing procedure related to the binomial distribution, test the

hypotheses in a. Does your conclusion agree with the conclusion reached in part a? c. When might the two approaches used in parts a and b not agree? 6.24 Refer to the data of Exercise 6.23.

a. Give the level of significance for your test. b. Place a 95 confidence interval on m

d . 6.25 Refer to the data of Exercise 6.11. A potential criticism of analyzing these data as if they were two independent samples is that the measurements taken in 1996 were taken at the same site as the measurements taken in 1982. Thus, there is the possibility that there will be a strong positive correlation between the pair of observations at each site.

a. Plot the pairs of observations in a scatterplot with the 1982 values on the horizontal

axis and the 1996 values on the vertical axis. Does there appear to be a positive correlation between the pairs of measurements? Estimate the correlation between the pair of observations?

b. Compute the correlation coefficient between the pair of observations.

Does this value confirm your observations from the scatterplot? Explain your answer.

c. Answer the questions posed in Exercise 6.11 parts a and b using a paired data

analysis. Are your conclusions different from the conclusions you reached treating the data as two independent samples? Engin. 6.26 Researchers are studying two existing coatings used to prevent corrosion in pipes that transport natural gas. The study involves examining sections of pipe that had been in the ground at least 5 years. The effectiveness of the coating depends on the pH of the soil, so the researchers recorded the pH of the soil at all 20 sites at which the pipe was buried prior to measuring the amount of corrosion on the pipes. The pH readings are given here. Describe how the researchers could conduct the study to reduce the effect of the differences in the pH readings on the evalua- tion of the difference in the two coatings’ corrosion protection. pH Readings at Twenty Research Sites Coating A 3.2 4.9 5.1 6.3 7.1 3.8 8.1 7.3 5.9 8.9 Coating B 3.7 8.2 7.4 5.8 8.8 3.4 4.7 5.3 6.8 7.2