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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 渭is 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=渭=05=0

05

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

We need to find the P渭-1鈮�x鈮�渭+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.

P渭-1鈮�x鈮�渭+1=P(78.6-1鈮�x鈮�78.6+1)=P(77.6鈮�x鈮�79.6)=35=0.06

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Most popular questions from this chapter

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.

Officer Salaries. Refer to Problem 5.

a. Use the answer you obtained in Problem 5(b)and Definition 3.11on page 140 to find the mean of the variable x^Interpret your answer.

b. Can you obtain the mean of the variable ix without doing the calculation in part (a)? Explain your answer.

Refer to Exercise 7.10 on page 295.

a. Use your answers from Exercise 7.10(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 7.10a).

Refer to Exercise 7.7 on page 295.

a. Use your answers from Exercise 7.7(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 7.7(a).

Teacher Salaries. Data on salaries in the public school system are published annually in Ranking of the States and Estimates of School Statistics by the National Education Association. The mean annual salary of (public) classroom teachers is \(55.4thousand. Assume a standard deviation of \)9.2thousand. Do the following tasks for the variable "annual salary" of classroom teachers.

a. Determine the sampling distribution of the sample mean for samples of size 64Interpret your answer in terms of the distribution of all possible sample mean salaries for samples of 64classroom teachers.

b. Repeat part (a) for samples of size256

c. Do you need to assume that classroom teacher salaries are normally distributed to answer parts (a) and (b)? Explain your answer.

d. What is the probability that the sampling error made in estimating the population means salary of all classroom teachers by the mean salary of a sample of 64classroom teachers will be at most \(1000?

e. Repeat part (d) for samples of size\)256
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