Chapter 18, Problem 28E

(a)

To determine

To describe the sampling distribution model for the sample mean if the sample size is small.

Explanation of Solution

In the question it is given that a sample is chosen randomly from a population that was strongly skewed to the left. Thus, the sampling distribution for the sample mean will also be skewed left. And the center will be at the mean $\mu$ and with the standard deviation $\frac{\sigma }{\sqrt{n}}$ as the spread of the distribution.

(b)

To determine

To explain what happens to the sampling distribution model’s shape, center and spread, if we make the sample larger.

Explanation of Solution

In the question it is given that a sample is chosen randomly from a population that was strongly skewed to the left. Thus, the sampling distribution for the sample mean will also be skewed left. And the center will be at the mean $\mu$ and with the standard deviation $\frac{\sigma }{\sqrt{n}}$ as the spread of the distribution. Thus, if we make the sample larger then, the sampling distribution will become more normal in shape but the center will still be centered at the mean $\mu$ and with the standard deviation $\frac{\sigma }{\sqrt{n_1}}$ as the spread of the distribution.

(c)

To determine

To explain what happens to the expected distribution of the data in the sample, as we make the sample large.

Answer to Problem 28E

The sample distribution should begin to more closely resemble the distribution of the population.

Explanation of Solution

In the question it is given that a sample is chosen randomly from a population that was strongly skewed to the left. Thus, the sampling distribution for the sample mean will also be skewed left. And the center will be at the mean $\mu$ and with the standard deviation $\frac{\sigma }{\sqrt{n}}$ as the spread of the distribution. Thus, as we make the sample large then, we increase the size of the sample, and the sample distribution should begin to more closely resemble the distribution of the population.