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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¯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¯is approximately normally distributed.

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Most popular questions from this chapter

A variable of a population has mean μ and standard deviationσ. 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?

The winner of the 2012-2013 National Basketball Association (NBA) championship was the Miami Heat. One possible starting lineup for that team is as follows.

a. Determine the population mean height, μ, of the five players:

b. Consider samples of size 2without replacement. Use your answer to Exercise 7.11(b)on page 295and Definition 3.11on page 140to find the mean, μr, of the variable x^.

c. Find μx*using only the result of part (a).

7.43 NBA Champs. Repeat parts (b) and (c) of Exercise 7.41 for samples of size 3. For part (b), use your answer to Exercise 7.13(b).

Explain why increasing the sample size tends to result in a smaller sampling error when a sample means is used to estimate a population mean.

Ethanol Railroad Tariffs. An ethanol railroad tariff is a fee charged for shipments of ethanol on public railroads. The Agricultural Marketing Service publishes tariff rates for railroad-car shipments of ethanol in the Biofuel Transportation Database. Assuming that the standard deviation of such tariff rates is \(1,150, determine the probability that the mean tariff rate of 500randomly selected railroad car shipments of ethanol will be within \)100of the mean tariff rate of all railroad-car shipments of ethanol. Interpret your answer in terms of sampling error.
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