remolatg

2021-03-09

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.

Nichole Watt

For this option (a):
This choice is appropriate since a larger sample size gives us more knowledge about the population and enables us to make more precise value predictions. This implies that if the predictions are more correct, the variability will decrease.
For choice (b)
This choice is accurate since the sample mean's variability over all potential samples and standard deviation of the sampling distribution of the sample mean are equal.
For choice (c)
This choice is accurate since the sample mean is an unbiased estimate of a population mean.
Option (d) is the best choice because the standard deviation of the sampling distribution provides the variance.
Option (e) is erroneous because the sampling distribution, which is the distribution of all potential sample means, cannot be centered around the sample mean (since there are many sample means).
Therefore, the right response is (e).

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