15. (EX) 5.19 The effect of increasing the sample size. Compute the mean and sta

Question

15. (EX) 5.19 The effect of increasing the sample size.

Compute the mean and standard deviation of the sampling distribution of the sample mean when you plan to take an SRS of size 49 from a population with mean 420 and standard deviation 21.

Now repeat the calculations for a sample size of 576.
Explain the effect of the increase on the sample mean and standard deviation. Generally, the mean and the standard deviation of the distribution of the sample mean are not affected by the sample size. As the sample size increases, the standard deviation of the distribution of the sample mean remains unchanged, and the mean gets further away from the population mean. As the sample size increases, the standard deviation of the distribution of the sample mean decreases and the mean remains unchanged. As the sample size increases, the standard deviation of the distribution of the sample mean increases and the mean remains unchanged.

Explanation / Answer

15. The population mean of the distribution of sample means is the same as the population mean of the distribution being sampled from. Thus the mean of the distribution of the means never changes. The standard deviation of the sample means, however, is the population standard deviation from the original distribution divided by the square root of the sample size. Thus as the sample size increases, the standard deviation of the means decreases; and as the sample size decreases, the standard deviation of the sample means increases.

As the sample size increases, the standard deviation of the distribution of the sample mean decreases and the mean remains unchanged.

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