Over a period of about nine months, 1,353 women
reported the timing of each of their menstrual cycles. For
the first cycle reported by each woman, the mean cycle
time was 28.86 days, and the standard deviation of the
1,353 times was 4.24 days.
(a) Construct a 92% confidence interval for the population
mean cycle time.
(b) Because environmental rhythms can influence biological
rhythms, one might hypothesize that the population
mean menstrual cycle time is 29.5 days, the
length of the lunar month. Is the confidence interval
of part (a) consistent with this hypothesis?