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Chapter 7: Q.7.31 (page 300)

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

Short Answer

Expert verified

The sampling error is indicated by the standard deviation of the sample mean (sampling error).

Step by step solution

01

Given Information

The standard deviation of the variablex.

02

Explanation

The standard error is the label given to the variable x's standard deviation.

Standard deviation, on the other hand, is a measure of dispersion. It gives a sense of how far the observations deviate from the mean value.

As a result, the sample standard deviation means The level of dispersion divergence of sample means from the mean of sample means, i.e. population means 渭, is shown by x.

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Most popular questions from this chapter

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.

Refer to Exercise 7.10on page 295.

a. Use your answers from Exercise 7.10(b)to determine the mean, 渭i, of the variable x^for each of the possible sample sizes.

b. For each of the possible sample sizes, determine the mean, 渭i+of the variable x^, using only your answer from Exercise 7.10(a)

A variable of a population has a mean of 渭=100and a standard deviation of蟽=28.

a. Identify the sampling distribution of the sample mean for samples of size 49.

b.In answering part (a), what assumption did you make about the distribution of the variable?

c. Can you answer part (a) if the sample size is 16instead of 49?

Why or why not?

NBA Champs Repeat parts (b) and (c) of Exercise 7.41 for samples of size 5. For part (b), use your answer to Exercise 7.15(b).

A variable of a population has mean 渭 and standard deviation蟽. that For a large sample size n, answer the following questions.

a. Identify the distribution ofx.

b. Does your answer to part (a) depend on n being large? Explain your answer.

c. Identify the mean and the standard deviation ofx.

d. Does your answer to part (c) depend on the sample size being large? Why or why not?
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