Question

. Fowle Marketing Research, Inc., bases charges to a client on the assumption that telephone surveys can be completed in a mean time of 15 minutes or less. If a longer mean survey time is necessary, a premium rate is charged. A sample of 35 surveys provided the survey times shown in the file named Fowle. Based upon past studies, the population standard deviation is assumed known with σ = 4 minutes. Is the premium rate justified?

(a). Formulate the null and alternative hypotheses for this application. (b). At α = 0.01, what is your conclusion? (c). What is your interpretation of the type II error for this problem? What is its impact on the firm? (d). What is the probability of making a Type II error when the actual mean time is 17 minutes? (e). Given α = 0.01, if the firm want to control the probability of making a type II error to be less than 0.05 when the actual mean time is more than 17 minutes, how large the sample size is needed?

Time
17
11
12
23
20
23
15
16
23
22
18
23
25
14
12
12
20
18
12
19
11
11
20
21
11
18
14
13
13
19
16
10
22
18
23