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Chapter 6: Q85E (page 367)

Suppose you want to estimate a population proportion,,pand,p^=.42,N=6000andn=1600.Find an approximate 95% confidence interval forp.

Short Answer

Expert verified

The approximate confidence interval for pis(0.399,0.441)

Step by step solution

01

Given information

p^=.42N=6000n=1600

Since,nN=0.2666>0.05

The finite population correction factor is used.

The estimated standard error is σ^p^

σ^p^=p^(1−p^)nN−nN=0.42(1−0.42)16006000−16006000=0.243616004,4006000=0.0123×0.8563=0.0105

The approximate confidence interval isp^±2σ^p^

p^±2σ^p^=0.42±(2×0.0105)=0.42±0.021=(0.399,0.441)

Therefore, the approximate 95%confidence interval forpis(0.399,0.441)

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