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Chapter 7: Q 6RP. (page 310)

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.

Short Answer

Expert verified

Part (a) The mean of the variable (x¯)is 18$1000s

Part (b) Yes.

Step by step solution

01

Part (a) Step 1: Given information

From the population of six officers, 15 size 4 samples are possible. The first column in the following table lists them.

02

Part (a) Step 2: Concept

Formula used:μx¯=∑x¯N

03

Part (a) Step 3: Calculation

Obtain the mean of the variable (x¯)

μx¯=∑x¯N=14+15+16+16+17+18+17+18+19+20+18+19+20+21+2215=27015=18

Thus, for sample size 4, the mean μx¯ of all potential sample mean wages is 18 $1000s.

04

Part (b) Step 1: Explanation

Yes, the mean of the variable (x¯) may be calculated because the mean for sampling sample means is the same as the population mean (μ) As a result, the population mean is $18.0 thousand dollars.

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Most popular questions from this chapter

Refer to Exercise 7.8 on page 295.

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

Refer to Exercise 7.7 on page 295.

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

Suppose that a simple random sample is taken without replacement from a finite population of size N.

Part (a): Show mathematically that Equations (7.1) and (7.2) are identical for samples of size 1.

Part (b): Explain in words why part (a) is true.

Part (c): Without doing any computations, determine r for samples of size N without replacement. Explain your reasoning.

Part (d): Use Equation(7.1) to verify your answer in part (c).
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