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

`hatp=400/2000=.2`

`n=2000`

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`

`.2-1.96sqrt((.2(.8))/2000)<p<.2+1.96sqrt((.2(.8))/2000)`

or approximately:

.1656<p<.2344

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

Sources:

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