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Chapter 6: Q84E (page 367)

Suppose you want to estimate a population mean,μ,and,x¯=422,s=14,N=375andn=40.Find an approximate 95% confidence interval forμ.

Short Answer

Expert verified

The approximate confidence interval forμ is(417.8164,426.1836) .

Step by step solution

01

Given information

x¯=422s=14N=375n=40

02

Calculate the approximate confidence interval forμ

nN=40375=0.1066

Since,nN=0.1066>0.05

The finite population correction factor is used.

The estimated standard error isσ^x¯

σ^x¯=sn(N−n)N=1440(375−40)375=2.2136×0.9451=2.0920

The approximate95% confidence interval isx¯±2σ^x¯

x¯±2σ^x¯=422±(2×2.092)=422±4.184=(417.8164,426.1836)

Therefore, the approximate 95%confidence interval forμis(417.8164,426.1836)

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