ATM machines have made it easier and quicker for customers to check account bala

Question

ATM machines have made it easier and quicker for customers to check account balances, transfer money, and obtain cash. Many banks are now considering the next generation of ATM machines that will feature news headlines, full-motion video, and tickets to events. In a random sample of 500 customers, 290 said that ATM machines should offer postage stamps. Fill in the blank. (Give your answer to two decimal places.)

The sample proportion of customers who believe that ATM machines should offer postage stamps is....

A 99% confidence interval for the true proportion of customers who believe that ATM machines should offer postage stamps is (,).

Explanation / Answer

a)

Note that              
              
p^ = point estimate of the population proportion = x / n = 290/500 =    0.58   [ANSWER]

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b)      
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.022072607          
              
Now, for the critical z,              
alpha/2 =   0.005          
Thus, z(alpha/2) =    2.575829304          
Thus,              
Margin of error = z(alpha/2)*sp =    0.056855269          
lower bound = p^ - z(alpha/2) * sp =   0.523144731          
upper bound = p^ + z(alpha/2) * sp =    0.636855269          
              
Thus, the confidence interval is              
              
(   0.523144731   ,   0.636855269   ) [ANSWER]

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