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Chapter 7: Q.8 (page 460)

Which of the following statements about the sampling distribution of the sample mean is incorrect? (a) The standard deviation of the sampling distribution will decrease as the sample size increases.

(b) The standard deviation of the sampling distribution is a measure of the variability of the sample mean among repeated samples.

(c) The sample mean is an unbiased estimator of the true population mean.

(d) The sampling distribution shows how the sample mean will vary in repeated samples.

(e) The sampling distribution shows how the sample was distributed around the sample mean

Short Answer

Expert verified

The correct answer is (e)

The incorrect statement is the sampling distribution shows how the sample was distributed around the sample mean

Step by step solution

01

Given Information

We have to find which of the statement is not correct

02

Explanation (a)

Consider, f option (a):

This option is correct because if a sample is larger, it provides more data about the population which allows us to predict more accurate values. This means that the variability decreases if the predictions are more accurate.

03

Explanation (b)

Consider option (b):

This option is correct because the standard deviation of a sampling distribution of a sample means and the variability of the sample mean over all possible samples are the same.

04

Explanation (c)

Consider option (c):

This option is correct because a population means has an unbiased estimator which is the sample mean.

05

Explanation (d)

Consider option (d):

This option is also correct because the variation is given by the standard deviation of the sampling distribution.

06

Explanation (e)

Consider option (e):

This option is not correct because the distribution of all possible sample mean is the sampling distribution and it cannot be centered on the sample mean (since there are many sample means.

Hence, the correct answer is (e).

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