Question

An auditor for a hardware store chain wished to compare the efficiency of two different auditing techniques. To do this he selected a sample of nine store accounts and applied auditing techniques A and B to each of the nine accounts selected. The number of errors found in each of techniques A and B is listed in the table below:

Errors in A	Errors in B
25	11
28	17
26	19
28	17
32	34
30	25
29	29
20	21
25	30

Does the data provide sufficient evidence to conclude that the number of errors in auditing technique A is greater than the number of errors in auditing technique B at the 0.1 level of significance? Select the [Alternative Hypothesis, Value of the Test Statistic]. (Hint: the samples are dependent)

a) [A > B, 1.976]

b) [μ_D > 0, 1.976]

c) [μ_D = 0, 1.976]

d) [μ_D ≥ 0, 1.976]

e) [μ_D > μ₁, 1.976]

f) None of the above

Answer 1

Solution:

An auditor for a hardware store chain wished to compare the efficiency of two different auditing techniques. To do this he selected a sample of nine store accounts and applied auditing techniques A and B to each of the nine accounts selected.

We have to test if the data provide sufficient evidence to conclude that the number of errors in auditing technique A is greater than the number of errors in auditing technique B.

Since samples are dependent, we use paired t test.

d = auditing technique A - auditing technique B

Since we would like to test auditing technique A > auditing technique B,

that is difference is auditing technique A - auditing technique B > 0

thus alternative hypothesis would be:

test statistic value:

where

Thus we need to make following table.

Errors in A	Errors in B	d=A - B	d^2
25	11	14	196
28	17	11	121
26	19	7	49
28	17	11	121
32	34	-2	4
30	25	5	25
29	29	0	0
20	21	-1	1
25	30	-5	25

Thus

Thus correct option is:

b) [μ_D > 0, 1.976]