The 90% confidence interval for the mean audit time is (3.583 ; 4.397) and it can be concluded that the mean audit time has increased since last year's audit time does not fall within the confidence interval.
Using calculator to calculate the sample mean and standard deviation :
The confidence interval can be calculated using the relation :
Since the sample size is small; we use a t-distribution ;
Lower boundary = 3.99 - 1.833(0.222) = 3.583
Upper boundary = 3.99 + 1.833(0.222) = 4.397
Therefore, the confidence interval estimate for the mean audit time is (3.583 ; 4.397)
B.)
Since the audit time recorded last year does not fall within the calculated confidence interval then the audit time has increased.
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