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 90% confidence interval for the true average menstrual cycle length.

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

(c) A researcher hypothesized that womens menstrual cycles are typically the same length as a lunar month - 29.5 days. Does your interval from (a) support this hypothesis?

(d) Are the assumptions for a confident interval met for this problem?

Please show complete work. PLEASE DON'T USE EXCEL.