Effect of n on the standard deviation. Refer to Exercise 1.40. To see the effect of sample size on the standard deviation of the sampling distribution of a statistic, combine pairs of samples (moving down the columns of the table) to obtain 25 samples of n = 12 measurements. Calculate the mean for each sample.
(a) Construct a relative frequency distribution for the 25 means. Compare this with the distribution prepared for Exercise 1.40 that is based on samples of n = 6 digits.
(b) Calculate the mean and standard deviation of the 25 means. Compare the standard deviation of this sampling distribution with the standard deviation of the sampling distribution in Exercise 1.40. What relationship would you expect to exist between the two standard deviations?