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Chapter 7: Q. 7.15 (page 295)

Repeat parts (b)-(e) of Exercise 7.11 for samples of size5.

Short Answer

Expert verified
  1. Part (b): Constructing the table of samples of size 5 of 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 1.

Part (e): The probability that x is within 1 inch of μis 1.

On interpreting, there is 100% change that the mean height of the four players selected will be within 1 inch of the population mean.

Step by step solution

01

Part (b) Step 1. Given information

Consider the given question,

02

Part (b) Step 2. Construct samples of size 5 of the given population.

The samples of size 5 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 7.86inches.

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 5is 1.

Px=μ=11=1

05

Part (e) Step 1. Find the probability that xwill 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)=11=1

On interpreting, we can say that there is 100%change that the mean height of the four players selected will be within 1 inch of the population mean.

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Most popular questions from this chapter

Poverty and Dietary Calcium. Calcium is the most abundant mineral in the human body and has several important functions. Recommendations for calcium are provided in Dietary Reference Intakes, developed by the Institute of Medicine of the National Academy of Sciences, The recommended adequate intake (RAI) of calcium for adults (ages 19-50) is 1000milligrams (mg) per day. If adults with incomes below the poverty level have a mean calcium intake equal to the RAI. what percentage of all samples of 18 such adults have mean calcium intakes of at most 947,4mg? Assume that σ=188mgState any assumptions that you are making in solving this problem.

7.35 Refer to Exercise 7.5 on page 295 .

a. Use your answers from Exercise 7.5(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, μ5, of the variable x¯, using only your answer from Exercise 7.5(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.

Population data: 3,4,7,8

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 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 most 0.5.

Officer Salaries. The following table gives the monthly salaries (in \(1000) of the six officers of a company.

a. Calculate the population mean monthly salary,μ

There are 15possible samples of size 4from the population of six officers. They are listed in the first column of the following table.

b. Complete the second and third columns of the table.

c. Complete the dot plot for the sampling distribution of the sample mean for samples of size 4Locate the population means on the graph.

d. Obtain the probability that the mean salary of a random sample of four officers will be within 1 (i.e., \)1000) of the population mean.
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