A church group is interested in estimating the true proportion of Americans who attend weekly religious services. How large a sample size is required to estimate the true proportion to within 3% with 95% confidence

  (b)  

We can use an estimatior for the population proportion as since we don't know previous info. And replacing into equation (b) the values from part a we got:

And rounded up we have that n=1068

Step-by-step explanation:

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 the confidence level is 99%, 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)  

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)  

We can use an estimatior for the population proportion as since we don't know previous info. And replacing into equation (b) the values from part a we got:

And rounded up we have that n=1068

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