1. Over 9 months, a random sample of 50 women were asked to record their average menstrual cycle length (in days). The sample average was 28.86 days, with a sample standard deviation of 4.24 days.

(a) Calculate the lower bound for the 90% confidence interval for the true average menstrual cycle length.

(b) Calculate the upper bound for the 90% confidence interval for the true average menstrual cycle length.

(c) Interpret the confidence interval found in (a,b) in terms of the problem.

(d) A researcher hypothesized that women's menstrual cycles are typically the same length as a lunar month - 29.5 days. Does your interval from (a,b) support this hypothesis? (e) Are the assumptions for a confident interval met for this problem?