Question

A company's average accounts receivable per customer is $132.54. After a problem in the automated accounting software is suspected, a random sample of 38 accounts reveals a sample mean of $143.55 and a sample standard deviation of $38.29.

After running a two-sided hypothesis test of the hypothesis that the average accounts receivable has changed, what is the best conclusion (using a 95% confidence level)?

Source

• There is not sufficient evidence that the average accounts receivable has changed.

• The average accounts receivable is still $132.54.

• The average accounts receivable has changed.

• The average accounts receivable is at least $143.55.

Answer 1

Solution :

= 132.54

= 143.55

s = 38.29

n = 38

This is the two tailed test .

The null and alternative hypothesis is

H₀ :   =132.54

H_a : 132.54

Test statistic = t

= ( - ) / s / n

= (143.55- 132.54) /38.29 / 38

= 1.773

p(t >1.773 ) = 1-P (t<1.773 ) = 0.0845

P-value = 0.0845

95% confidence level

= 0.05  

0.0845 > 0.05

Do not reject the null hypothesis.

There is not sufficient evidence that the average accounts receivable has changed.