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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¯equals the mean of the variable under consideration. That is, μx¯=μ.

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

7.49 Mobile Homes. 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~ denote the mean price of a sample of new mobile homes.
a. For samples of size 50, find the mean and standard deviation of x¯. Interpret your results in words.
b. Repeat part (a) with n=100.

Repeat parts (b)-(e) of Exercise 7.11 for samples of size5.

You have seen that the larger the sample size, the smaller the sampling error tends to be in estimating a population means by a sample mean. This fact is reflected mathematically by the formula for the standard deviation of the sample mean: σi=σ/n. For a fixed sample size, explain what this formula implies about the relationship between the population standard deviation and sampling error.

Population data: 1,2,3

Part (a): Find the mean, μ,of the variable.

Part (b): For each of the possible sample sizes, construct a table similar to Table 7.2on the page 293and draw a dotplot for the sampling for the sampling distribution of the sample mean similar to Fig 7.1on page 293.

Part (c): Construct a graph similar to Fig 7.3and interpret your results.

Part (d): For each of the possible sample sizes, find the probability that the sample mean will equal the population mean.

Part (e): For each of the possible sample sizes, find the probability that the sampling error made in estimating the population mean by the sample mean will be 0.5or less, that is, that the absolute value of the difference between the sample mean and the population mean is at most 0.5.

Women at Work. In the article "Job Mobility and Wage Growth" (Monthly Labor Review. Vol. 128. No. 2, pp. 33-39).

A. Light examined data on employment and answered questions regarding why workers separate from their employers. According to the article, the standard deviation of the length of time that women with one job are employed during the first 8 years of their career is 92 weeks. Length of time employed during the first 8 years of a career is a left-skewed variable. For that variable, do the following tasks.

a. Determine the sampling distribution of the sample mean for simple random samples of 50 women with one job. Explain your reasoning.

b. Obtain the probability that the sampling error made in estimating the mean length of time employed by all women with one job by that of a random sample of 50 such women will be at most 20 weeks.
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