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Chapter 7: Q. 7.14 (page 295)

Repeat parts (b)-(e) of Exercise 7.11 for samples of size4.

Short Answer

Expert verified

Part (b): Constructing the table of samples of size 4of the given population is given below,


Part (c): The dot plot is given below,


Part (d): The chance that sample mean is equal to population mean is 0.

Part (e): The probability that x is within 1 inch of μis localid="1652610198587" 0.06.

Step by step solution

01

Part (b) Step 1. Given information

Consider the given question,

02

Part (b) Step 2. Construct samples of size 4 of the given population.

The samples of size 4 and the corresponding means are obtained,

Here, Chrish Bosh by B, Dwyane Wade by W, LeBron James by J, Mario Chalmers by C and Udonis Haslem H.

03

Part (c) Step 1. Construct the dot plot.

On constructing the dot plot for the sampling distribution of the sample mean,

04

Part (d) Step 1. Find the chance that the sample mean will equal the population mean.

Consider the previous question,

The population mean height for five players is 78.6inches.

From table obtained in part (b), it is clear that none of the sample means are equal to the population mean. Also, number of samples of size 4is 5.

Px=μ=05=0

05

Part (e) Step 1. Find the probability that x will be within 1 inch of μ.

We need to find the Pμ-1≤x≤μ+1.

From the table obtained in part (b), it is clear that none of the sample means are within 1 inch of the population mean.

Pμ-1≤x≤μ+1=P(78.6-1≤x≤78.6+1)=P(77.6≤x≤79.6)=35=0.06

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Most popular questions from this chapter

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).

Young Adults at Risk. Research by R. Pyhala et al. shows that young adults who were born prematurely with very low birth weights (below 1500 grams) have higher blood pressure than those born at term. The study can be found in the article. "Blood Pressure Responses to Physiological Stress in Young Adults with Very Low Birth Weight" (Pediatrics, Vol. 123, No, 2, pp. 731-734 ). The researchers found that systolic blood pressures, of young adults who were born prematurely with very low birth weights have mean 120.7 mm Hg and standard deviation 13.8 mm Hg.
a. Identify the population and variable.
b. For samples of 30 young adults who were born prematurely with very low birth weights, find the mean and standard deviation of all possible sample mean systolic blood pressures. Interpret your results in words.
c. Repeat part (b) for samples of size 90.

You have seen that the larger the sample size, the smaller the sampling error tends to be in estimating a population means by a sample mean. This fact is reflected mathematically by the formula for the standard deviation of the sample mean: σi=σ/n. For a fixed sample size, explain what this formula implies about the relationship between the population standard deviation and sampling error.

Population data: 2,3,5,7,8

Part (a): Find the mean, μ, of the variable.

Part (b): For each of the possible sample sizes, construct a table similar to Table 7.2on the page localid="1652592045497" 293and draw a dotplot for the sampling for the sampling distribution of the sample mean similar to Fig 7.1on page 293.

Part (c): Construct a graph similar to Fig 7.3and interpret your results.

Part (d): For each of the possible sample sizes, find the probability that the sample mean will equal the population mean.

Part (e): For each of the possible sample sizes, find the probability that the sampling error made in estimating the population mean by the sample mean will be 0.5or less, that is, that the absolute value of the difference between the sample mean and the population mean is at most0.5.

Taller Young Women. In the document Anthropometric Reference Data for Children and Adults, C. Fryer et al. present data from the National Health and Nutrition Examination Survey on a variety of human body measurements. A half-century ago, the mean height of (U.S.) women in their 20s was 62.6 inches. Assume that the heights of today's women in their 20s are approximately normally distributed with a standard deviation of 2.88 inches. If the mean height today is the same as that of a half-century ago, what percentage of all samples of 25 of today"s women in their 20s have mean heights of at least 64.24 inches?
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