Refer to the menstrual cycle data of Exercise 6.S.6.
(a) Over the entire time period of the study, the women reported a total of 12,247 cycles. When all of these cycles are included, the mean cycle time is 28.22 days. Explain why one would expect that this mean would be smaller than the value 28.86 given in Exercise 6.S.6. (b) Instead of using only the first reported cycle as in Exercise 6.S.6, one could use the first four cycles for each woman, thus obtaining 1,353 × 4 = 5,412 observations. One could then calculate the mean and standard deviation of the 5,412 observations and divide the SD by √5412 to obtain the SE; this would; yield a much smaller value than the SE found in Exercise 6.S.6. Why would this approach not valid?