Question

Menstrual cycle length. Menstrual cycle lengths (days) in an SRS of ten women are as follows: {31, 28, 26, 24, 29, 33, 25, 26, 28, 30}. Use this data to test whether mean menstrual cycle length differs significantly from a lunar month. (A lunar month is 29.5 days.) Assume that population values vary according to a Normal distribution. Use a two-sided alternative and 5% significance level. Note that ?̅=28.0 days with standard deviation s = 2.8284 days.

Question 2. True or False: The null hypothesis is that the mean menstrual length is equal to 29.5 days.

a. True

b. False

Question 3. What is the test statistic?

a. -1.68

b. -0.53

c. 0.53

d. 1.68

Question 4. What is the degrees of freedom of the test statistic?

a. 7

b. 8

c. 9

d. 10

Question 5. What is the two-sided p-value associated with your test statistic?

a. 0.01 < P < 0.02

b. 0.02 < P < 0.05

c. 0.05 < P < 0.10

d. 0.10 < P < 0.20

Question 6. What is your decision?

a. Reject H0

b. Retain (do NOT reject) H0

Question 7. Interpretation in the context of the study?

a. The average menstrual length is significantly different from 29.5 days

b. The average menstrual length is not significantly different from 29.5 days

Question 8. What would the one-sided p-value be for the previous problem? (refer to Question 5 and remember how one-sided and two-sided p-values are related)

a. 0.01 < P < 0.02

b. 0.02 < P < 0.05

c. 0.05 < P < 0.10

d. 0.10 < P < 0.20

Question 9. The previous problem calculated the mean length of menstrual cycles in an SRS of n = 10 women. The data revealed ?̅=28.0 days with standard deviation s = 2.8284 days.

What is a 95% confidence interval for the mean menstrual cycle length?

a. 28.0 ± (2.228)(0.8944)

b. 28.0 ± (2.228)(2.8284)

c. 28.0 ± (2.262)(0.8944)

d. 28.0 ± (2.262)(2.8284)

Question 10. Based on the confidence interval you just calculated, is the mean menstrual cycle length significantly different from 25 days at α = 0.05 (two sided)? Is it significantly different from μ = 30 days at the same α-level? (Chapter 10.4 considered the relationship between confidence intervals and significance tests. The same rules apply here.)

a. It is not significantly different from 25 days and not significantly different from 30 days

b. It is not significantly different from 25 days, but it is significantly different from 30 days

c. It is significantly different from 25 days, but not significantly different from 30 days

d. It is significantly different from 25 days and significantly different from 30 days

Answer 1