Question

One of the major measures of the service quality of any organization is the speed with which it responds to customer complaints. A large department store is reviewing its service quality in last year. Last year, there were 30 complaints. The following data (including 30 numbers) represents 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

5.1 Construct a 95% confidence interval estimate of the mean number of days between the receipt of a complaint and the resolution of the complaint.

You can use Excel to calculate the std and mean of the sample, but please use a calculator and tables for the rest of your answer. Please submit all of your calculations, Excel printouts, and the final answer. Please justify all steps in your solution.

Answer 1

using excel

data
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
Mean =	55.83333
sample standard deviation =	48.77258

here we will use t-test to find the confidence interval.

from t table,

t at 95 % with 30-1 = 29 degree of freedom is 2.05

95 % CI = $\bar{x} \pm t_{0.05}\frac{s}{\sqrt{n}}$

=$55.83\pm 2.05*\frac{48.77}{\sqrt{30}}$

= $55.83\pm 18.25$

= 37.58 , 74.08

95% confidence interval estimate of the mean number of days between the receipt of a complaint and the resolution of the complaint is 7.58 , 74.08