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Chapter 7: Q. 7.45 (page 301)

7.45 NBA Champs. Repeat parts (b) and (c) of Exercise 7.41for samples of size 5. For part (b). use your answer to Exercise 7.15(b).

Short Answer

Expert verified

The mean height (μx¯)for samples of size 5is 78.6.

Step by step solution

01

Given information

To determine the sample size of 5. The sample from exercise 7.41is:

02

Explanation

For samples of size 5, calculate the mean height (μx¯).
As a result, the size 5samples and their means are obtained as given in the table below:

Sample size
Height
Mean(x)
B,W,J,C,H
83,76,80,74,80
83+76+80+74+805=78.6

As a result, the number of possible samples (N)of size 5 is one.
The mean of all possible sample means is calculated as follows for samples of size 5:
μx¯=∑x¯iN

=78.61

=78.6

As a result, the mean height (μx¯)for size 5samples is 78.6.

03

Explanation

Calculate the mean height μx¯.
The average height of five players in the population is 78.6 inches.
The population mean is equal to the mean of the sample mean.
That is to state,
μx¯=μ
=78.6
Asa result, the mean height ( (μx¯) for samples of size 5 is 78.6.

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Most popular questions from this chapter

7.47 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 is3369 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 size400.

A variable of a population has a mean of μ=35and a standard deviation of σ=42.

a. If the variable is normally distributed, identify the sampling distribution of the sample mean for samples of size 9.

b. Can you answer part (a) if the distribution of the variable under consideration is unknown? Explain your answer.

c. Can you answer part (a) if the distribution of the variable under consideration is unknown but the sample size is 36instead of 9?

Why or why not?

7.49 Mobile Homes. 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~ denote the mean price of a sample of new mobile homes.
a. For samples of size 50, find the mean and standard deviation of x¯. Interpret your results in words.
b. Repeat part (a) with n=100.

In Example 7.5, we used the definition of the standard deviation of a variable to obtain the standard deviation of the heights of the five starting players on a men's basketball team and also the standard deviation of x for samples of sizes 1,2,3,4,5.The results are summarized in Table 7.6on page 298. Because the sampling is without replacement from a finite population, Equation (7.1) can also be used to obtain σx.

Part (a): Apply Equation (7.1) to compute σx for sample sizes of 1,2,3,4,5. Compare your answers with those in Table 7.6.

Part (b): Use the simpler formula, Equation (7.2) to compute σx for samples of sizes 1,2,3,4,5.Compare your answers with those in Table 7.6. Why does Equation (7.2)generally yield such poor approximations to the true values?

Part (c): What percentages of the population size are samples of sizes 1,2,3,4,5.

A variable of a population is normally distributed with mean μand standard deviation σ. For samples of size n, fill in the blanks. Justify your answers.

a. Approximately 68%of all possible samples have means that lie within of the population mean, μ

b. Approximately 95%of all possible samples have means that lie within of the population mean, μ

c. Approximately 99.7%of all possible samples have means that lie within of the population mean, μ

d. 100(1-α)%of all possible samples have means that lie within _of the population mean, μ(Hint: Draw a graph for the distribution of x, and determine the z-scores dividing the area under the normal curve into a middle 1-αarea and two outside areas ofα/2
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