The First National Bank of Wilson has 620 checking account c

The First National Bank of Wilson has 620 checking account customers. A recent sample of 50 of these customers showed 28 to have a Visa card with the bank.

Construct the 99 percent confidence interval for the proportion of checking account customers who have a Visa card with the bank. (Round your answers to 3 decimal places.)

Confidence interval for the proportion of checking account customers who have a Visa card with the bank is ____ and ____.

Solution

p=28/50=0.56

Given a=1-0.99=0.01, Z(0.005) = 2.58 (from standard normal table)

So the lower bound is

p - Z*sqrt(p*(1-p)/n) =0.56-2.58*sqrt(0.56*(1-0.56)/50) =0.3788847

So the upper bound is

p + Z*sqrt(p*(1-p)/n) =0.56+2.58*sqrt(0.56*(1-0.56)/50) =0.7411153