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Chapter 6: Q24E (page 348)

Question: Explain the differences in the sampling distributions of xfor large and small samples under the following assumptions.

a. The variable of interest, x, is normally distributed.

b. Nothing is known about the distribution of the variable x.

Short Answer

Expert verified

Answer

a. No difference

b. Sample distribution will be if the size is large and remain unknown if the size is small.

Step by step solution

01

Whenever the variable of interest remains normally distributed

a.

If the variable of interest remains normally distributed, the sample size will not affect the sampling distribution in this case. Therefore, the sampling distribution will be and will be normal.

02

Determination of the differences when nothing is known

b.

In this case, the sampling distribution will remain at whenever the sample size will remain large which means when the sample size will be above 30. T the sampling distribution will remain unknown whenever the sample size remains less than 30.

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