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, what is the true proportion of all local residents...

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, what is the true proportion of all local residents who are Perry Como fans? Estimate at the 95% confidence level

Expert Answers
jeew-m eNotes educator| Certified Educator

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%.