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Chapter 7: Q. 7.29 (page 300)

Does the sample size have an effect on the standard deviation of all possible sample means? Explain your answer.

Short Answer

Expert verified

Yes, the sample size has an effect on the standard deviation 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 standard deviation of all possible sample means.

02

Step 2. Explanation

For samples of size n,the standard deviation of the variable x炉equals the standard deviation of the variable under consideration divided by the square root of the sample size. That is, 蟽x炉=蟽n.

So, it can be seen that the standard deviation of all possible sample means depends on the sample size n.

And it can be seen that as the sample size increase the standard deviation ofx炉decreases.

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Most popular questions from this chapter

According to the U.S. Census Bureau publication Manufactured Housing Statistics, the mean price of new mobile homes is \(65,100. Assume a standard deviation of \)7200. Let x denoted the mean price of a sample of new mobile homes.

Part (a): For samples of size 50, find the mean and standard deviation of x. Interpret your results in words.

Part (b): Repeat part (a) with n=100.

Refer to Exercise 7.9 on page 295.

a. Use your answers from Exercise 7.9(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 7.9(a).

America's Riches. Each year, forbes magazine publishes a list of the richest people in the United States. As of September l6, 2013, the six richest Americans and their wealth (to the neatest billion dollars) are as shown in the following table. Consider these six people a population of interest.

(a) For sample size of 4construct a table similar to table 7.2 on page293.(There are 15 possible sample of size 4

(b) For a random sample of size 4determine the probability that themean wealth of the two people obtained will be within 3(i.e,3billion) of the population mean. interpret your result in terms of percentages.

Worker Fatigue. A study by M. Chen et al. titled "Heat Stress Evaluation and Worker Fatigue in a Steel Plant (American Industrial Hygiene Association, Vol. 64. Pp. 352-359) assessed fatigue in steelplant workers due to heat stress. If the mean post-work heart rate for casting workers equals the normal resting heart rate of 72beats per minute (bpm), find the probability that a random sample of 29 casting workers will have a mean post-work heart rate exceeding 78.3bpm Assume that the population standard deviation of post-work heart rates for casting workers is 11.2 bpm. State any assumptions that you are making in solving this problem.

Does the sample size have an effect on the mean of all possible sample means? Explain your answer.
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