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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炉equals the mean of the variable under consideration. That is, 渭x炉=渭.

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

7.2 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?

Why is obtaining the mean and standard deviation of x炉 a first step in approximating the sample distribution of the sample mean by a normal distribution?

Baby Weight. The paper "Are Babies Normal?" by T. Clemons and M. Pagano (The American Statistician, Vol. 53, No, 4. pp. 298-302) focused on birth weights of babies. According to the article, the mean birth weight is 3369 grams (7 pounds, 6.5 ounces) with a standard deviation of 581 grams.
a. Identify the population and variable.
b. For samples of size 200, find the mean and standard deviation of all possible sample mean weights.
c. Repeat part (b) for samples of size 400.

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:

Part (a): Find the population mean height of the five players.

Part (b): For samples of size 2, construct a table similar to Table 7.2 on page 293. Use the letter in parentheses after each player's name to represent each player.

Part (c): Draw a dotplot for the sampling distribution of the sample mean for samples of size 2.

Part (d): For a random sample of size2, what is the chance that the sample mean will equal the population mean?

Part (e): For a random sample of size 2, obtain the probability that the sampling error made in estimating the population mean by the sample mean will be1 inch or less; that is, determine the probability that x will be within1 inch of 渭. Interpret your result in terms of percentages.

The following graph shows the curve for a normally distributed variable. Superimposed are the curves for the sampling distributions of the sample mean for two different sample sizes.

a. Explain why all three curves are centered at the same place.

b. Which curve corresponds to the larger sample size? Explain your answer.

c. Why is the spread of each curve different?

d. Which of the two sampling-distribution curves corresponds to the sample size that will tend to produce less sampling error? Explain your answer.

c. Why are the two sampling-distribution curves normal curves?
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