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Chapter 8: Q 8.96 (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 greatest confidence level, given that the margin of error is to be kept at half year. Recall thatσ=12.1 years.

Short Answer

Expert verified

The confidence level is78.5%.

Step by step solution

01

Given Information

It is given that

n=900

σ=12.1

E=0.5

02

Determination of Confidence Level

We know that confidence level is given by

E=za2σn

0.5=za212.1900

za2=0.590012.1

role="math" localid="1652726923958" za2=1.24

From tables, confidence level for za2=1.24is 0.1075.

Also,

Confidence level, α2=0.1075

α=0.215

Also,

100(1-α)%=100(1-0.215)%

=78.5%

Therefore, required confidence level is78.5%

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What is meant by saying that a 1-αconfidence interval is

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