Question

Given that accounts receivable can be one of the following: current, late and uncollectible. Industry standards show that 57 percent of accounts receivable are current, 31 percent are late and 12 percent are uncollectible. A local law firm has 454 accounts receivable in which 251 are current, 155 are late and 48 are uncollectible.

Category	fo	fe	(fo - fe)2 / fe
current	251	258.7800	0.2339
late	155	140.7400	1.4448
Uncollectible	48	54.4800	0.7707

a)

Select the appropriate hypothesis and decision rule using a 0.020 significance level.

	Hypotheses:   H0: 12 percent of the observations are in current, 57 percent are in late and 31 percent are in Uncollectible   H1: Distribution is not as above. Decision Rule:   Reject H0 if X2 > 9.21.
	Hypotheses:   H0: 57 percent of the observations are in current, 31 percent are in late and 12 percent are in Uncollectible   H1: Distribution is not as above. Decision Rule:   Reject H0 if X2 > 7.824.
	Hypotheses:   H0: 12 percent of the observations are in current, 57 percent are in late and 31 percent are in Uncollectible   H1: Distribution is not as above. Decision Rule:   Reject H0 if X2 > 7.378.
	Hypotheses:   H0: 57 percent of the observations are in current, 31 percent are in late and 12 percent are in Uncollectible   H1: Distribution is not as above. Decision Rule:   Reject H0 if X2 < 7.824.

b) Compute the value of the test statistic.

For full marks your answer should be accurate to at least two decimal places.

Test statistic: 0

c)

What is your decision regarding H₀.

	Reject H0.
	Do not Reject H0.
	Can not be determined based on our results.

Answer 1

Categories :

current, late and uncollectible.

Degrees of freedom = Number of a categories -1 = 3-1 =2

: Significance level = 0.02

Critical value : for 2 degrees of freedom = 7.824

(a)

Hypotheses:
  H₀: 57 percent of the observations are in current, 31 percent are in late and 12 percent are in Uncollectible
  H₁: Distribution is not as above.
Decision Rule:
  Reject H₀ if > 7.824

b)

test statistic

Test Statistic = 2.4494

c)

As : < Critical value :7.824; Do not Reject H_o

Answer

Do not Reject H₀.