Complete parts (a) through (e) for the population data below 6, 8, 10, 12 O A. A

Question

Complete parts (a) through (e) for the population data below 6, 8, 10, 12 O A. As the sample size increases, the sampling distribution of the sample mean clusters closer to the population mean. O B. As the sample size decreases, the sampling distribution of the sample mean clusters closer to the population mean. ° C. As the sample size increases, there are more possible distinctsamples. 0 D. The plot appears random d. For each of the possible sample sizes, find the probability that the sample mean will equal the population mean. Probability 4 4 4 (Type integers or simplified fractions.) e. For each of the possible sample sizes, find the probability that the sampling error made in estimating the population mean by the sample mean wil be 0.5 or less (in magnitude), that is, that the absolute value of the difference between the sample mean and the population mean is at most 0.5. Probability 4

Explanation / Answer

As the sample size increases, the sampling distribution of the sample means comes closer and closer to the population mean.

d) Population mean = 9

For each of the sample sizes, the sample means are computed as:

e) Solved in above table ( last column )

n Samples possible Sample means Probability d) Probability e) 1 6, 8, 10, 12 6, 8, 10, 12 0 0 2 (6, 8), (6, 10), (6, 12), (8, 10), (8, 12), (10, 12) 7, 8, 9, 9, 10, 11 2/6 = 0.3333 1/3 = 0.3333 3 (6, 8, 10), (8, 10, 12), (6, 8, 12) 8, 10, 26/3 0 1/3 = 0.3333 4 (6, 8, 10, 12) 9 1 1

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