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Chapter 7: Q. 7.26 (page 300)

Although, in general, you cannot know the sampling distribution of the sample mean exactly, by what distribution can you often approximate it?

Short Answer

Expert verified

The sampling distribution of the sample mean is often approximated using the normal distribution.

Step by step solution

01

Step 1. Introduction

For a variable x and a given sample size, the distribution of the variable x炉is called the sampling distribution of a sample mean.

It is the distribution of all possible sample means for samples of a given size.

02

Step 2. Explanation

Generally, the value of sampling distribution of a sample mean is not known exactly.

But the value can be often approximated by a normal distribution.

That is under certain conditions, the variable x炉is approximately normally distributed.

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Most popular questions from this chapter

A variable of a population has a mean of 渭=35and a standard deviation of 蟽=42.

a. If the variable is normally distributed, identify the sampling distribution of the sample mean for samples of size 9.

b. Can you answer part (a) if the distribution of the variable under consideration is unknown? Explain your answer.

c. Can you answer part (a) if the distribution of the variable under consideration is unknown but the sample size is 36instead of 9?

Why or why not?

According to the central limit theorem, for a relatively large sample size, the variable x~is approximately normally distributed.

a. What rule of thumb is used for deciding whether the sample size is relatively large?

b. Roughly speaking, what property of the distribution of the variable under consideration determines how large the sample size must be for a normal distribution to provide an adequate approximation to the distribution of x~ ?

7.1 Why is sampling often preferable to conducting a census for the purpose of obtaining information about a population?

Refer to Fig. 7.6on page 306 .

a. Why are the four graphs in Fig. 7.6(a) all centered at the same place?

b. Why does the spread of the graphs diminish with increasing sample size? How does this result affect the sampling error when you estimate a population mean, 渭by a sample mean, x~ ?

c. Why are the graphs in Fig. 7.6(a) bell shaped?

d. Why do the graphs in Figs. 7.6(b)and (c) become bell shaped as the sample size increases?

7.2 Why should you generally expect some error when estimating a parameter (e.g., a population mean) by a statistic (e.g., a sample mean)? What is this kind of error called?
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