Awell-known bank credit card firm wishes to estimate the proportion of credit card holders who carry a nonzero balance at the end of the month and incur an interest charge. assume that the desire margin of error is 0.03 at 98% confidence.
a) how large a sample should be selected if it is anticipated that roughly 70% of the firm's card holders carry a nonzero balance at the end of the month?
b) how large a sample should be selected if no planning value for the proportion could be specified?

a) 1267

b)  1509

Step-by-step explanation:

As per given , we have

Significance level :

Using the z-value table , the critical z value for 98% confidence :

Margin of error : E= 0.03

Formula for sample size :

, where p is the prior estimate of population proportion.

a) p=0.70

Sample size :

Simplify , we get

Hence, the minimum sample size required = 1267

a) if no estimate of prior population proportion is given , we take p= 0.5

Sample size :

Simplify , we get

Hence, the minimum sample size required = 1509