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Chapter 8: Q 8.95 (page 334)

Civilian Labor Force. Consider again the problem of estimating the mean age, μ, of all people in the civilian labor force. In Example 8.7on page 328 , we found that a sample size of 2250 is required to have a margin of error of 0.5year and a 95% confidence level. Suppose that, due to financial constraints, the largest sample size possible is 900 . Determine the smallest margin of error, given that the confidence level is to be kept at 95%. Recall thatσ=12.1 years.

Short Answer

Expert verified

The margin of error is0.791year.

Step by step solution

01

Given Information

It is given that σ=12.1

n=900

Confidence level is 95%

za2=1.96

02

Determination of Margin of Error

The margin of error is given by

E=za2σn

=1.9612.1900

=0.791

Hence, margin of error is0.791

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Most popular questions from this chapter

Corporate Farms. The U.S. Census Bureau estimates the mean value of the land and buildings per corporate farm. Those estimates are published in the Census of Agriculture, Suppose that an estimate, x, is obtained and that the margin of error is \(1000. Does this result imply that the true mean. μ, is within \)1000 of the estimate? Explain your answer.

A simple randoes sample is taken from a population and yields the following data for a variable of the population:

Find a point estimatate for the population mean.(i.e, the mean of the variable)

Venture-Capital Investments. In Exercise 8.69, you found a 95%confidence interval for the mean amount of all venture-capital investments in the fiber optics business sector to be from \(5.389million to\)7.274million. Obtain the margin of error by

a. taking half the length of the confidence interval.

b. using Formula 8.1on page 325. (Recall that and that σ=$2.04million.)

Assume that the population standard deviation is known and decide weather use of the zinterval procedure to obtain a confidence interval for the population mean is reasonable. Explain your answers.

The variable under consideration is very close to being normally distributed, and the sample size is75.

One-Sided One-Mean z-Intervals. Presuming that the assumptions for a one-mean z-interval are satisfied, we have the following formulas for (1-α)-level confidence bounds for a population mean \(\mu\) :

- Lower confidence bound: x~-zσ·σ/n

- Upper confidence bound: x¯+zα·σ/n

Interpret the preceding formulas for lower and upper confidence bounds in words.
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