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. Suppose a sample of 35 surveys produces the data in the Microsoft Excel Online file below. Use a known σ = 3.7 minutes. Is the premium rate justified?

1. Formulate the null and alternative hypotheses for this application.

   H₀: μ _________greater than or equal to 15greater than 15less than or equal to 15less than 15equal to 15not equal to 15

   H_a: μ _________greater than or equal to 15greater than 15less than or equal to 15less than 15equal to 15not equal to 15

2. Compute the value of the test statistic (to 2 decimals).

3. What is the p-value (to 4 decimals)?

4. Using ? = .01, is a premium rate justified for this client?

20.3
13.7
16.2
18.1
14.2
17.3
14.6
17.4
18.5
9.6
15.1
16.6
17
14.5
19.6
11.3
16.3
20.5
21.7
15.5
12.2
18.5
25.9
14.5
21.6
15.6
15.9
14.7
17.6
18
16.7
11.6
16.8
13
13.2

Answer 1