Question

An accountant believes that the percentage of accounts that will be uncollectible increase as the ages of the accounts increase. To test his theory, the accountant randomly selects independent samples of 500 accounts with ages between 31- 60 days and 500 accounts with ages between 61-90 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 31-60 days were eventually classified as uncollectible while 27 of the 500 accounts with ages between 61-90 days were eventually classified as uncollectible. Does the percentage of accounts that will be uncollectible increase as the age of the accounts increase? Use α =0.10.

Type out the complete hypothesis test (Be sure to label all steps) and write out the complete conclusion including your alpha level, test statistic value and p-value. Also make sure to include a critical value and what the rejection region would be.

Answer 1

The hypothesis being tested is:

H₀: p₁ = p₂

H_a: p₁ < p₂

p1	p2	pc
0.02	0.054	0.037	p (as decimal)
10/500	27/500	37/1000	p (as fraction)
10.	27.	37.	X
500	500	1000	n
	-0.034	difference
	0.	hypothesized difference
	0.0119	std. error
	-2.85	z
	.0022	p-value (one-tailed, lower)

The critical value is 1.645.

The rejection region is z > 1.645.

The p-value is 0.0022.

Since the p-value (0.0022) is less than the significance level (0.10), we can reject the null hypothesis.

Therefore, we can conclude that the percentage of accounts that will be uncollectible increase as the age of the accounts increase.