The Evergreen Company operates retail pharmacies in 10 eastern states. Recently, the company's internal audit
department selected a random sample of 300 prescriptions issued throughout the system. The objective of the
sampling was to estimate the average dollar value of all prescriptions issued by the company. The following data were
collected: x = $14.23 s = 3.00 a. Determine the 90% confidence interval estimate for the true average sales value for
prescriptions issued by the company. Interpret the interval estimate. b. One of its retail outlets recently reported that
it had monthly revenue of $7,392 from 528 prescriptions. Are such results to be expected? Do you believe that the
retail outlet should be audited? Support your answer with calculations and logic.
(a)
Data:
n
300
x-bar
14.23
s
3
%
90
Standard Error, SE = s/√n = 0.1732
Degrees of freedom = 299
t- score = 1.6500
Width of the confidence interval = t * SE = 0.2858
Lower Limit of the confidence interval = x-bar - width = 13.9442
Upper Limit of the confidence interval = x-bar + width = 14.5158
The confidence interval is [$13.94 $14.52]
Interpretation:
If samples of size 300 are repeatedly drawn from the population and the confidence intervals constructed
such intervals will contain the true mean 90% of the time.
(b) In this case, x-bar = 7392/528 = 14
Since $14 lies within the confidence interval calculated above, we cannot suspect the result. No audit is required.