Suppose that every day for 3 months bill takes a random samp

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 averages to her histogram of the sampling distriubtion 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?

Solution

a)

Yes, because they are both sampling distirbutions of means, which is approximated normally distributed according to central limit theorem.

b)

Yes, becausethey refer to the sample population. The central limit theorem states that the center of the distrbutions of sample means is the population mean, so we can expect they have the same center.

c)

No, because their sample sizes are different. The central limit theorem implies that larger sample sizes make the spread of the sampling distribution of means to be smaller.