Last year a company received 50 complaints concerning carpet installation. The data in the accompanying table represents the number of days between the receipt of a complaint and the resolution of the complaint.
57 62 2 31 139 30 21 154 5 118
83 74 29 17 14 130 111 111 27 86
82 33 25 30 2 14 8 164 32 36
23 24 25 1 16 20 10 12 16 13
27 53 40 27 37 26 27 21 31 65
a. The supervisor claims that the mean number of days between the receipt of a complaint and the resolution of the complaint is 20 days. At the 0.01 level of significance, is there evidence that the claim is not true (that is, that the mean number of days is different from 20)?
b. What assumption about the population distribution is needed in order to conduct the t test in (a)?
c. Construct a normal probability plot to evaluate the assumption made in (b).
d. Do you think that the assumption needed in order to conduct the t test in (a) is valid?