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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

The value of σx, depends on the sample size n. if we change nthe value ofσx i.e. standard deviation of all possible sample means differs.

Step by step solution

01

Given Information 

We have to find The sample size have an effect on the standard deviation of all possible sample means.

02

Explanation

σx=N-nN-1·σnσnif the sample is drawn without replacement.

if the sample is drawn with replacement:

Where

n=SamplesizeN=populationsize

The value of σx, depends on the sample size n. if we change nthe value of σxi.e. standard deviation of all possible sample means differs.

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Most popular questions from this chapter

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 6construct a table similar to table 7.2 on page293 what is the relationship between the only possible sample here and the population?

(b) For a random sample of size 6determine the probability that themean wealth of the two people obtained will be within 3(i.e,3 billion) of the population mean. interpret your result in terms of percentages.

Refer to Exercise 7.10on page 295.

a. Use your answers from Exercise 7.10(b)to determine the mean, μi, of the variable x^for each of the possible sample sizes.

b. For each of the possible sample sizes, determine the mean, μi+of the variable x^, using only your answer from Exercise 7.10(a)

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, μs, of the variable x¯for each of the possible sample sizes.

b. For each of the possible sample sizes, determine the mean, μs, of the variable x¯, using only your answer from Exercise 7.9(a).

7.67 Brain Weights. In 1905, R. Pearl published the article "Biometrical Studies on Man. 1. Variation and Correlation in Brain Weight" (Biometrika, Vol. 4, pp. 13-104). According to the study, brain weights of S wedish men are normally distributed with a mean of 1.40kg and a standard deviation of 0.11kg

a. Determine the sampling distribution of the sample mean for samples of size 3 Interpret your answer in terms of the distribution of all possible sample mean brain weights for samples of three Swedish men.

b. Repeat part (a) for samples of size 12

c. Construct graphs similar to those shown in Fig. 7.4on page 304 .

d. Determine the percentage of all samples of three Swedish men that have mean brain weights within 0.1kg of the population mean brain weight of 1.40kg. Interpret your answer in terms of sampling error.

e. Repeat part (d) for samples of size 12
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