A direct-mail sales company must determine its credit policies quite carefully.

Question

A direct-mail sales company must determine its credit policies quite carefully. Suppose that the firm suspects that advertisements in a certain magazine have led to an excessively high rate of write-offs (accounts regarded as uncollectable). The firm wants to establish a 90% confidence interval for this magazine's write-off proportion that is accurate to 0.02. a) How many accounts must be sampled to guarantee this goal? b) If this many (the sample size n computed in part a) accounts are sampled and 10% of the sampled accounts are determined to be write offs, what is the resulting 90% confidence intervals?

Explanation / Answer

a.
Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)
Z a/2 at 0.1 is = 1.645
Sample Proportion = 0.5
ME = 0.02
n = ( 1.645 / 0.02 )^2 * 0.5*0.5
= 1691.266 ~ 1692
              
b.
Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)
Z a/2 at 0.1 is = 1.645
Sample Proportion = 0.1
ME = 0.02
n = ( 1.645 / 0.02 )^2 * 0.1*0.9
= 608.856 ~ 609

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