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?

20.3
13.7
16.2
18.1
14.3
17.3
14.6
17.4
18.5
10.2
15.1
16.6
17
14.5
20.2
11.3
16.3
20.5
21.7
15.6
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

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

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

Answer 1

= (20.3 + 13.7 + 16.2 + 18.1 + 14.3 + 17.3 + 14.6 + 17.4 + 18.5 + 10.2 + 15.1 + 16.6 + 17 + 14.5 + 20.2 + 11.3 + 16.3 + 20.5 + 21.7 + 15.6 + 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)/35 = 16.43

a) The test statistic is

  

b) P-value = P(Z > 2.29)

= 1 - P(Z < 2.29)

= 1 - 0.9890

= 0.0110