In the book Cases in Finance, Nunnally and Plath present a case in which the estimated percent-age 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. An accountant believes that the percentage of accounts that will be uncollectible increases as the ages of the accounts increase. To test this theory, the accountant randomly selects independent samples of 500 accounts with ages between 31 and 60 days and 500 accounts with ages between 61 and 90 days from the accounts receivable ledger dated one year ago. When the sampled accounts are examined, it is found that 10 of the 500 accounts with ages between 31 and 60 days were eventually classified as uncollectible, while 27 of the 500 accounts with ages between 61 and 90 days were eventually classified as uncollectible. Let p1 be the proportion of accounts with ages between 31 and 60 days that will be uncollectible and let p2 be the proportion of accounts with ages between 61 and 90 days that will be uncollectible.
a. Use the MINITAB output below to determine how much evidence there is that we should reject H0: p1 – p2 = 0 in favor of Ha: p1 – p2 ≠ 0.
b. Identify a 95 percent confidence interval for p1 – p2, and estimate the smallest that the difference between p1 and p2 might be.