In the book Cases in Finance, Nunnally and Plath present a case in which the estimated percentage of uncollectible accounts varies with the age of the account. Here the age of an unpaid account is the number of days elapsed since the invoice date.
Suppose an accountant believes the percentage of accounts that will be uncollectible increases as the ages of the accounts increase. To test this theory, the accountant randomly selects 500 accounts with ages between 31 and 60 days from the accounts receivable ledger dated one year ago. The accountant also randomly selects 500 accounts with ages between 61 and 90 days from the accounts receivable ledger dated one year ago.
a. If 10 of the 500 accounts with ages between 31 and 60 days were eventually classified as uncollectible, find a point estimate of and a 95 percent confidence interval for the proportion of all accounts with ages between 31 and 60 days that will be uncollectible.
b. If 27 of the 500 accounts with ages between 61 and 90 days were eventually classified as uncollectible, find a point estimate of and a 95 percent confidence interval for the proportion of all accounts with ages between 61 and 90 days that will be uncollectible.
c. Based on these intervals, is there strong evidence that the percentage of accounts aged between 61 and 90 days that will be uncollectible is higher than the percentage of accounts aged between 31 and 60 days that will be uncollectible? Explain.