Menstrual cycle length. Problem 3 calculated the mean length of menstrual cycles in an SRS of 9 women. The data revealed days with standard deviation s = 2.906 days.

a)Calculate a 95% confidence interval for the mean menstrual cycle length.

= 27.78 s = 2,906n = 9t = 2.306

95% CI for = 27.78 2.306 (2.906) = 27.78 2.23 = (25.55 to 30.01)

b)Based on the confidence interval you just calculated, is the mean menstrual cycle length significantly different from 28.5 days at = 0.05 (two sided)? Is it significantly different from = 30 days at the same -level? Explain your reasoning. (Section 10.4 in your text considered the relationship between confidence intervals and significance tests. The same rules apply here.)