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 wished to study this part of their customer service for each department. For the 50 complaints made to the carpeting department last year, the following data represent the number of days between the receipt of the complaint and its resolution.
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 26 36 20 23 33 68
The carpeting department supervisor claims that the average number of days between the receipt of a complaint and its resolution is 20 days or less.
a. What are the null and alternative hypotheses for testing whether the installation supervisor's claim is valid?
b. Using the data above, carry out that test for a significance level of 5% and for a significance level of 1%