Menstrual cycle length. Menstrual cycle lengths (days) in an SRS of nine women are as follows: {31, 28, 26, 24, 29, 33, 24, 27, 28}. a) Use these data to test whether mean menstrual cycle length differs significantly from a lunar month (29.5 days). Assume the population values vary according to a Normal distribution, use a two-sided alternative, and show all hypothesis testing steps. b) Calculate a 95% confidence interval for the mean menstrual cycle length. c) Based on the confidence interval you just constructed, is the mean menstrual cycle length significantly different from 28.5 days at alpha=0.05 (two-sided)? Is it significantly different from mu=30 days at alpha=0.05? Explain