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
27	13
30	19
28	21
30	19
34	36
32	27
31	31
22	23
27	32

Does the data provide sufficient evidence to conclude that the number of errors in auditing technique A is different from the number of errors in auditing technique B at the 0.05 level of significance? Select the [Alternative Hypothesis, Value of the Test Statistic]. (Hint: the samples are dependent)

a) [μ_D ≠ 0, 1.976]

b) [μ_D ≠ μ₁, 1.976]

c) [μ_D = 0, 1.976]

d) [μ_D ≥ 0, 1.976]

e) [A ≠ B, 1.976]

Answer 1

Option a) is correct answer. let we see how to solve it,

Hypothesis:-  

H₀: μD = 0

H₁: μD ≠ 0    (two-tailed)

Test Statistics:-

  

Where, D = Error in B - Error in A

= Mean of all dirrerence

= standard error of the mean difference

Calculation:-

By using Ms- Excel calculation the value of test statistics is,

t = 1.976

The p - value is,

p value = 0.084

Interpretation :- Here p value is greater than the given level of significance α = 0.05. Hence we accept the null hypothesis.

Since, data provide sufficient evidence to conclude that the number of errors in auditing technique A is different from the number of errors in auditing technique B at the 0.05 level of significance.