Question

One of the major measures of the quality of service provided by any organization is the speed with which it responds to customer complaints. A large family-held department store selling furniture and flooring, including carpet, had undergone a major expansion in the past several years. In particular, the flooring department had expanded from 2 installation crews to an installation supervisor, a measurer, and 15 installation crews. Last year, there were 50 complaints concerning carpet installation. The following data, also in the file FURNITURE, represent the number of days between the receipt of a complaint and the resolution of the complaint: 54 5 35 137 31 27 152 2 123 81 74 27 11 19 126 110 110 29 61 35 94 31 26 5 12 4 165 32 29 28 29 26 25 1 14 13 13 10 5 27 4 52 30 22 36 26 20 23 33 68 Problem 4 Please continue for problem questions…

a. Construct and interpret a 95% confidence interval estimate of the population mean number of days between the receipt of a complaint and the resolution of the complaint and interpret. Use Minitab

b. What assumption must you make about the population distribution in order to construct the confidence interval estimate in (a)?

c. Do you think that the assumption needed in order to construct the confidence interval estimate in (a) is valid? Explain.

Answer 1

Part a

Required 95% confidence interval by using Minitab is given as below:

Variable          N      Mean     StDev   SE Mean

Days             50     43.04     41.93      5.93

Variable             95.0% CI           

Days          (   31.12,   54.96)    

Confidence interval = (31.12, 54.96)

Part b

The assumption of normality we must make about the population distribution in order to construct the above confidence interval.

Part c

Yes, assumption needed in order to construct the confidence interval is valid because the variable number of days between the receipt of a complaint and resolution of the complaint follows an approximate normal distribution.