Chapter 7, Problem 8PT

To determine

The correct statement which is incorrect from the options about the sampling distribution of the sample mean (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 distributions shows how the sample was distributed around the sample mean.

Answer to Problem 8PT

The correct answer is (e).

Explanation of Solution

Here, for option (a):

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

For option (b):

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

For option (c):

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

For option (d):

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

For option (e):

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

Hence, the correct answer is (e).