You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable estimate for the population proportion. You would like to be 90% confident that you esimate is within 2.5% of the true population proportion. How large of a sample size is required

And rounded up we have that n=1076

Step-by-step explanation:

Information given

represent the desired margin of error

Solution

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by  and . And the critical value would be given by:

The margin of error for the proportion interval is given by this formula:  

   (a)  

We can assume that the best estimate for the true proportion is . And on this case we have that and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

  (b)  

And replacing into equation (b) the values from part a we got:

And rounded up we have that n=1076

it would be 6xy and -16xy.