A major brand credit card firm is interested in estimating a Proportion of its c

Question

A major brand credit card firm is interested in estimating a Proportion of its credit card holders that carry a non-zero balance at the end of the month and incur an interest charge.
A firm wants this estimate to be to within 3% with 98% Confidence.

Question 1: What is a minimum required Sample size for estimating a Proportion of credit card holders with non-zero balance at the end of the month if, according to current firm’s records,
70% of its credit card holders carry a non-zero balance at the end of the month?

632 credit card holders
897 credit card holders
1,263 credit card holders
None of the above

Question 2: What is a minimum required Sample size for estimating a Proportion of credit card holders with non-zero balance at the end of the month if no estimate of a Sample Proportion is available?

1,068 credit card holders
1,503 credit card holders
752 credit card holders
None of the above

Explanation / Answer

1) margin of error E =0.03

p=0.7

and for 98% CI, z=2.326

hence sample size n=p(1-p)*(Z/E)2  =1263

2)for no estimate p=0.5

hence sample size n=p(1-p)*(Z/E)2  =1503

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