n=2000,x=400, 95% confidenceUse the sample data and confidence level to construct the confidence interval estimate of the population proportion p.



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Posted on (Answer #1)

95% confidence level implies `alpha=.05,alpha/2=.025`



The confidence interval we seek is `hatp-z_(alpha/2)sqrt((hatp(1-hatp))/n)<p<hatp+z_(alpha/2)sqrt((hatp(1-hatp))/n)`

From a table, `z_(alpha/2)=z_(.025)=1.96`


or approximately:


So p lies between 16.6% and 23.4% with a 95% confidence level.


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