Exercise 10.1

1.

From Rasmussen, Statistics with Data Analyses, CA: Brooks-Cole. Investigators wanted to compare the drugs morphine and nalbuphine on their effect in changing pupil size. So they selected 11 volunteers and randomly assigned 6 of them to several does of morphine and the other 5 to several doses of nalbuphine. Before receiving the drug their pupil sizes were measured. After waiting a prescribe amount of time after the dosages of the drugs they measured the change in diameters of the subjects pupils. The data are:

      Treatment    Change in pupil diameter
      Morphine     .08   .8  1.0   1.9   2.0   2.4
      Nalbuphine   -.3   .0   .2    .4    .8

(a)

Obtain comparison dotplots of the data. Comment.

(b)

Let $\Delta$ be the effect of the different drugs on pupil size (morphine minus nalbuphine). We want to test

• H₀: $\Delta = 0$ versus
• H_A: $\Delta \ne 0$

Obtain the Wilcoxon test statistic and compare it to what we would expect under Ho. Use class code, Two-Sample Hypothesis and CI (Wilcoxon) , to determine the p-value. Conclude in terms of the problem.

(c)

Obtain the estimate of and a confidence interval for the effect, using the Wilcoxon. Conclude in terms of the problem.

2.

Suppose we wanted to investigate the difference in the thicknesses of a pages in two books, but all we had was a ruler with eighths-of-inches. Set up an experimental design to do this. (Note you can measure the thickness of a bunch of pages even though you cannot measure a page). What plots could you use here? What are the parameters of interest? What are the hypotheses? What analysis would you use?

3.

From Rasmussen, Statistics with Data Analyses, CA: Brooks-Cole. Researchers wanted to study the effect of regular alcohol assumption on plasma estrogen. The participants in the experiment were 20 adult male squirrel monkeys, of similar age and good health (What variables are being controlled here?). They randomly divided the monkeys into two equal sized groups. Monkeys in the alcohol group consumed a steady diet of 12% ethyl alcohol while those in the control group had the same diet with no alcohol. The results are:

      Alcohol:  3.17   2.52   2.59   4.25  3.27  4.92  
                5.46   2.83   4.80   2.26

      Control   6.57   5.81   5.63   5.75   4.54  5.35
                4.16   5.12   4.69   4.52

(a)

Obtain comparison dotplots of the data. Comment.

(b)

Let $\Delta$ be the effect of the different drugs on pupil size (morphine minus nalbuphine). We want to test

• H₀: $\Delta = 0$ versus
• H_A: $\Delta \ne 0$

Obtain the Wilcoxon test statistic and compare it to what we would expect under Ho. Use class code, Two-Sample Hypothesis and CI (Wilcoxon) , to determine the p-value. Conclude in terms of the problem.

(c)

These sort of experiments produced what warning level?

2000-08-26