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Chapter 7: Q. 7.13 (page 295)

Repeat parts (b)-(e) of Exercise 7.11 for samples of size3.

Short Answer

Expert verified

Part (b): Constructing the table of samples of size 1 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 0.

Part (e): The probability that x is within 1 inch of 渭is localid="1652609280028" 0.5.

Step by step solution

01

Part (b) Step 1. Given information

Consider the given question,

02

Part (b) Step 2. Construct samples of size 3 of the given population.

The samples of size 3 and the corresponding means are obtained,

Here, Chrish Bosh is represented by B, Dwyane Wade is represented by W, LeBron James is represented by J, Mario Chalmers is represented by C and Udonis Haslem is represented by 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 3is 10.

Px=渭=010=0

05

Part (e) Step 1. Find the probability that xwill be within 3 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 3 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)=510=0.5

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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, 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 7.9(a).

Early-Onset Dementia. Dementia is the loss of intellectual and social abilities severe enough to interfere with judgment, behavior, and daily functioning. Alzheimer's disease is the most common type of dementia. In the article "Living with Early Onset Dementia: Exploring the Experience and Developing Evidence-Based Guidelines for Practice" (Al=hcimer's Care Quarterly, Vol. 5, Issue 2, pp. 111-122), P. Harris and J. Keady explored the experience and struggles of people diagnosed with dementia and their families. If the mean age at diagnosis of all people with early-onset dementia is 55 years, find the probability that a random sample of 21 such people will have a mean age at diagnosis less than 52.5 years. Assume that the population standard deviation is 6.8 years. State any assumptions that you are making in solving this problem.

7.46 Young Adults at Risk. Research by R. Pyhala et al. shows that young adults who were born prematurely with very low birth weights (below 1500grams) 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 120.7mmHgand standard deviation 13.8mmHg.
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 .

Refer to Exercise 7.8 on page 295.

a. Use your answers from Exercise 7.8(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 7.8(a).

Refer to Exercise 7.10on page 295.

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

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