An auditor for a hardware store chain wished to compare the

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

Select a 90% confidence interval for the true mean difference in the two techniques.

Solution

CI = x1 - x2 ± t a/2 * Sqrt ( sd1 ^2 / n1 + sd2 ^2 /n2 )
Where,
x1 = Mean of Sample 1, x2 = Mean of sample2
sd1 = SD of Sample 1, sd2 = SD of sample2
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x1)=29
Standard deviation( sd1 )=3.5
Sample Size(n1)=9
Mean(x2)=24.55
Standard deviation( sd2 )=7.451
Sample Size(n1)=9
CI = [ ( 29-24.55) ±t a/2 * Sqrt( 12.25/9+55.517401/9)]
= [ (4.45) ± t a/2 * Sqrt( 7.5297) ]
= [ (4.45) ± 1.86 * Sqrt( 7.5297) ]
= [-0.6539 , 9.5539]