The First National Bank of Wilson has 700 checking account customers. A recent s

Question

The First National Bank of Wilson has 700 checking account customers. A recent sample of 70 of these customers showed 28 have a Visa card with the bank.

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

Confidence interval for the proportion is between  and .

The First National Bank of Wilson has 700 checking account customers. A recent sample of 70 of these customers showed 28 have a Visa card with the bank.

Explanation / Answer

Solution:

Given a=1-0.99=0.01, Z(0.005) = 2.575 (from standard normal table)

p=28/70 = 0.4

So the lower bound is

p-Z*sqrt(p*(1-p)/n) = 0.4-2.575*sqrt(0.4 *(1-0.4)/70) = 0.249

So the upper bound is

p+Z*sqrt(p*(1-p)/n) = 0.4+2.575*sqrt(0.4 *(1-0.4)/70) = 0.551

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