a Suppose that a random sample of size 2 is to be selected w

(a) Suppose that a random sample of size 2 is to be selected without replacement from this population. There are 12 possible samples (provided that the order in which observations are selected is taken into account):

Compute the sample mean for each of the 12 possible samples.

Use this information to construct the sampling distribution of x. (Display the sampling distribution as a density histogram.)

(b) Suppose that a random sample of size 2 is to be selected, but this time sampling will be done with replacement. Using a method similar to that of Part (a), construct the sampling distribution of x. Hint: There are 16 different possible samples in this case. (Enter the probabilities as fractions.)

20, 23	20, 26	20, 29	23, 20	23, 26	23, 29
26, 20	26, 23	26, 29	29, 20	29, 23	29, 26

20 + 23 +26 + 29 24.5

Solution

Sample Sample Mean Sample Sample Mean 20, 23 21.5 26, 20 23 20, 26 23 26, 23 24.5 20, 29 24.5 26, 29 27.5 23, 20 21.5 29, 20 24.5 23, 26 24.5 29, 23 26 23, 29 26 29, 26 27.5 141 153 Column Sample Mean Probability A 21.5 1/6 B 23 1/6 C 24.5 1/4 D 26 1/6 E 27.5 1/6 1    With repitition Column Sample Mean Probability a 20 1/8 b 21.5 1/8 c 23 3/16 d 24.5 1/8 e 26 3/16 f 27.5 1/8 g 29 1/8 1