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Chapter 8: Q 8.51 (page 330)

A confidence interval for a population mean has length 20.

a. Determine the margin of error.

b. If the sample mean is 60, obtain the confidence interval.

c. Construct a graph that illustrates your results.

Short Answer

Expert verified

a. Margin of error is 10.

b. Confidence interval length is role="math" localid="1652632332836" 50,70.

c.

Step by step solution

01

Given Information

It is given that Length of confidence interval is 20and sample mean is60.

02

a. Determination of Margin of Error.

Length of population mean L=20

Margin of Error=12脳20

Margin of Error=10

03

b. Determination of Confidence Interval

Confidence interval = Point estimate + Margin of error

=60卤10

=(60-10,60+10)

=(50,70)

04

c. Graph

The graph is as below:

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Most popular questions from this chapter

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

The sample data contain outliers, and the sample size is20.

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

The sample data contain no outliers, the sample size is 250, and the variable under consideration is far from being normally distributed.

Civilian Labor Force. Consider again the problem of estimating the mean age, 渭, 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 greatest confidence level, given that the margin of error is to be kept at half year. Recall that蟽=12.1 years.

Explain the difference between a point estimate of a parameter and a confidence-interval estimate of a parameter.

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 \(1000. Does this result imply that the true mean. 渭, is within \)1000 of the estimate? Explain your answer.
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