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Chapter 7: Q. 7.28 (page 300)

Does the sample size have an effect on the mean of all possible sample means? Explain your answer.

Short Answer

Expert verified

No, the sample size does not have an effect on the mean of all possible sample means.

Step by step solution

01

Step 1. Given Information

We need to identify whether the sample size has an effect on the mean of all possible sample means.

02

Step 2. Explanation

For any sample size, the mean of all possible sample means equals the population mean.

For samples of size n, the mean of the variable x炉equals the mean of the variable under consideration. That is, 渭x炉=渭.

So, for every sample size, the sample mean is equal to the population mean and it does not depend on the sample size.

As a result, the sample size does not have an effect on the mean of all possible sample means.

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Most popular questions from this chapter

According to the U.S. Census Bureau publication Manufactured Housing Statistics, the mean price of new mobile homes is \(65,100. Assume a standard deviation of \)7200. Let x denoted the mean price of a sample of new mobile homes.

Part (a): For samples of size 50, find the mean and standard deviation of x. Interpret your results in words.

Part (b): Repeat part (a) with n=100.

What is another name for the standard deviation of the variable x ? What is the reason for that name?

America's Richest. Explain what the dotplots in part (c) of exercise 7.17-7.22 illustrate about the impact of increasing sample size on sampling error.

Refer to Exercise 7.5 on page 295.

a. Use your answers from Exercise 7.5(b) to determine the mean, 渭s, of the variable x炉for each of the possible sample sizes.

b. For each of the possible sample sizes, determine the mean, 渭s, of the variable x炉, using only your answer from Exercise 7.5(a).

Repeat parts (b)-(e) of Exercise 7.11 for samples of size4.
See all solutions

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