The number of books sold over the course of the four-day book fair were 174, 171, 259, and 67. Assume that samples of size 2 are randomly selected with replacement from this population of four values. Identify the probability of each sample, and describe the sampling distribution of the sample means.

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Asked Dec 3, 2019
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The number of books sold over the course of the four-day book fair were 174, 171, 259, and 67. Assume that samples of size 2 are randomly selected with replacement from this population of four values. Identify the probability of each sample, and describe the sampling distribution of the sample means.

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Expert Answer

Step 1

Total number of possible samples =4*4 =16 (As 4 choices for each value).

As all sample occur with equal probability, probability of each sample =1/16 (0.0625).

Below is sampling distribution of mean.

...
х1
p(x1,x2) sample mean
х2
174
174
0.0625
174
174
171
0.0625
172.5
0.0625
174
259
216.5
174
67
0.0625
120.5
171
174
0.0625
172.5
171
171
0.0625
171
171
259
0.0625
215
171
67
119
0.0625
259
174
0.0625
216.5
171
259
0.0625
215
259
259
259
0.0625
259
67
0.0625
163
67
174
0.0625
120.5
171
67
0.0625
119
67
259
0.0625
163
67
67
0.0625
67
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х1 p(x1,x2) sample mean х2 174 174 0.0625 174 174 171 0.0625 172.5 0.0625 174 259 216.5 174 67 0.0625 120.5 171 174 0.0625 172.5 171 171 0.0625 171 171 259 0.0625 215 171 67 119 0.0625 259 174 0.0625 216.5 171 259 0.0625 215 259 259 259 0.0625 259 67 0.0625 163 67 174 0.0625 120.5 171 67 0.0625 119 67 259 0.0625 163 67 67 0.0625 67

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