## Related questions with answers

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.

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 $p_1$ be the proportion of accounts with ages between $31$ and $60$ days that will be uncollectible, and let $p_2$ be the proportion of accounts with ages between $61$ and $90$ days that will be uncollectible.

Use the Minitab output below to determine how much evidence there is that we should reject $H_0: p_1-p_2=0$ in favor of $H_a: p_1-p_2 \neq 0$.

$\begin{array}{lcccl} \text {Sample } & \mathrm{X} & \mathrm{N} & \text { Sample } \mathrm{p} & \\ 1 \text { (31 to } 60 \text { days) } & 10 & 500 & 0.020000 & \text { Difference }=\mathrm{p}(1)-\mathrm{p}(2) \\ 2 \text { (61 to 90 days } & 27 & 500 & 0.054000 & \text { Estimate for difference: }-0.034 \\ 95 \% \text { CI for difference: }(-0.0573036,-0.0106964) & \\ \text {Test for difference }=0 \text { (vs not }=0): \quad Z=-2.85 & \text { P-Value }=0.004 \end{array}$

Solution

VerifiedThe goal of this task is to test the null and the alternative hypothesis. Hypotheses that will help us try to determine is there a difference between the proportion of two accounts being uncollected, is this a null hypothesis

$H_0: \mu_1-\mu_2 = 0,$

and this alternative hypothesis:

$H_a: \mu_1-\mu_2 \neq 0.$

We will test this using $\alpha$ and $p$-value.

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