Suppose that every day for 3 months Bill takes a random sample of 20 college students, records the number of calories they consume on that day, finds the average of the 20 observations, and adds the average to his histogram of the sampling distribution of the mean.
Suppose also that every day for 2 months Susan takes a random sample of 30 college students and records the number of calories they consume on that day (which is fairly symmetric), finds the average of the 30 observations, and adds the average to her histogram of the sampling distribution of the mean.
(a) Can we expect Bill's distribution and Susan's distribution to have the same shape? Why or why not? If not, how will the shapes differ?
(b) Can we expect Bill's distribution and Susan's distribution to have the same center? Why or why not? If not, how will the centers differ?
(c) Can we expect Bill's distribution and Susan's distribution to have the same spread? Why or why not? If not, how will the spreads differ?