In preparing a report on the economy, we need to estimate the percentage of businesses that plan to hire additional employees in the next 60 days. a) How many randomly selected employers must we contact in order to create an estimate in which we are 98% confident with a margin of error of 5%? b) Suppose we want to reduce the margin of error to 3%. What sample size will suffice? c) Why might it not be worth the effort to try to get an interval with a margin of error of 1%?

a)  

And rounded up we have that n=543

b)    

And rounded up we have that n=1509

c)    

And rounded up we have that n=13573

Step-by-step explanation:

For this case since we don't have previous info we can assume that the best estimator for the true proportion is

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

   (a)  

Part a

The significance level is The critical value would be for this case:

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=543

Part b

And rounded up we have that n=1509

Part c

And rounded up we have that n=13573