Find the 90% confidence interval for the mean cost of selected pairs of shoes. H

Question

Find the 90% confidence interval for the mean cost of selected pairs of shoes. He selects a random sample of 36 pairs of shoes from a catalog and finds the following costs (in dollars) as shown below.            

          60           70           75          55            80          55

                      50            40           80          70            50          95

                     120           90           75          85            80          60

                     110           65            80         85            85          45

                       75           60            90         90            60          95

                      110          85            45         90            70          70

Explanation / Answer

sample mean=75

sample standard deviation=19.16097

Given a=1-0.9=0.1, Z(0.05) = 1.645 (from standard normal table)

So the lower bound is

xbar - Z*s/vn =75 -1.645*19.16097/sqrt(36 ) =69.7467

So the upper bound is

xbar + Z*s/vn =75 +1.645*19.16097/sqrt(36 ) =80.2533

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