4) 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.

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

Answer to question 3 if helpful for question 4 )

Sample Mean; x = 27.78

Sample Standard Deviation; s = 2.91

t-statistic = (x - ) / (s / n^0.5)

t-statistic = (27.78 - 29.5) / (2.91 / 9^0.5)

= -1.7732

p-value = 0.114163