# n=200, x=40, 95%confidence   Use the sample data and confidence level to construct the confidence interval estimate of the population proportion p. A confidence of 95% implies that `alpha=.05,alpha/2=.025`

`hatp=40/200=.2`

`n=200`

`z_(alpha/2)=1.96` from a table.

The interval we seek is given by:

`hatp-z_(alpha/2)sqrt((hatp(1-hatp))/n)<p<hatp+z_(alpha/2)sqrt((hatp(1-hatp))/n)`

Thus:

`.2-1.96sqrt((.2(.8))/200)<p<.2+1.96sqrt((.2(.8))/200)`  or approximately:

.1446<p<.2554

Thus, with 95% confidence, we can say that 14.5%<p<25.5%

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A confidence of 95% implies that `alpha=.05,alpha/2=.025`

`hatp=40/200=.2`

`n=200`

`z_(alpha/2)=1.96` from a table.

The interval we seek is given by:

`hatp-z_(alpha/2)sqrt((hatp(1-hatp))/n)<p<hatp+z_(alpha/2)sqrt((hatp(1-hatp))/n)`

Thus:

`.2-1.96sqrt((.2(.8))/200)<p<.2+1.96sqrt((.2(.8))/200)`  or approximately:

.1446<p<.2554

Thus, with 95% confidence, we can say that 14.5%<p<25.5%