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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

Teacher Salaries. Data on salaries in the public school system are published annually in Ranking of the States and Estimates of School Statistics by the National Education Association. The mean annual salary of (public) classroom teachers is \(55.4thousand. Assume a standard deviation of \)9.2thousand. Do the following tasks for the variable "annual salary" of classroom teachers.

a. Determine the sampling distribution of the sample mean for samples of size 64Interpret your answer in terms of the distribution of all possible sample mean salaries for samples of 64classroom teachers.

b. Repeat part (a) for samples of size256

c. Do you need to assume that classroom teacher salaries are normally distributed to answer parts (a) and (b)? Explain your answer.

d. What is the probability that the sampling error made in estimating the population means salary of all classroom teachers by the mean salary of a sample of 64classroom teachers will be at most \(1000?

e. Repeat part (d) for samples of size\)256

Population data: 1,2,3,4.

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

Part (b): For each of the possible sample sizes, construct a table similar to Table 7.2on the page 238and 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.

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

NBA Champs Repeat parts (b) and (c) of Exercise 7.41 for samples of size 4. For part (b), use your answer to Exercise 7.14(b).

Refer to Exercise 7.4 on page 295.

a. Use your answers from Exercise 7.4(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 7.4(a).
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