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Fifty-six percent of respondents to an online poll said that they were Perry Como fans. If 982 randomly selected people responded to this poll,...

For 95% confidence interval we can calculate the true proportion as;


`P = barp+-1.96sqrt((barp(1-barp))/n)`


Where;


P = true proportion of perry como fans


`barp` = Observed proportion of perry como fans


n = sample size


In the above equation 1.96 stands for 95% confidence interval. 


If you need 90% confidence interval you should use 1.65 and for 99% confidence interval 2.58 respectively.



According to our data;


`barp = 56% = 0.56`


`n = 982`



`P = 0.56+-1.96sqrt((0.56(1-0.56))/982)`


For upper range P = 0.576 = 57.6%


For lower range P = 0.544 = 54.4%



So the true proportion of perry como fans is between 54.4%-57.6%.

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