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# The following data are the length of the menstrual cycle in a random sample of 15 women.

INSTRUCTIONS TO CANDIDATES

Show work on all problems. Remember to always state your hypotheses, decision rules, and conclusions with interpretations. In total no more than 5 pages

Only neatly written or typed papers will be graded. SAS or R only should be used for all questions.

1. The following data are the length of the menstrual cycle in a random sample of 15 women. Test the hypothesis that the mean length of human menstrual cycle is equal to a lunar month (=29.5 days). The data are 26, 24, 29, 33, 25, 26, 23, 30, 31, 30, 28, 27, 29, 26, and 28 days. (15 points).

2. Using the following data, clearly state your hypothesis, test the null hypothesis that male and female turtles have the same mean serum cholesterol concentrations, and clearly state your conclusion. (15 points).

Male Female

220.1 223.4

218.6 221.5

229.6 230.2

228.8 224.3

222.0 223.8

224.1 230.8

226.5

3. Using data of the Question 2, if the null hypothesis is rejected, what are the 95% confidence limits for the averages of male and female, and their difference. If The null hypothesis is not rejected, compute the 95% confidence limits for the common population mean. Clearly state your conclusions. (15 points).

4. The experimental data of Question 2 might have been collected to determine whether serum cholesterol concentrations varied as much in male turtles as in female turtles. With those

data, use the variance-ratio test to assess π»0: π2 = π2 versus π»π΄: π2 ≠ π2 .

Clearly state your conclusions. (15 points).

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