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 = 3.5 minutes. Is the premium rate justified?

Call Time (minutes)

20.3

13.7

16.2

18.1

13.8

17.3

14.6

17.4

18.5

10.5

15.1

16.6

17

14.5

20

11.3

16.3

20.5

21.7

16

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

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

H₀: μ ? ___

H_a: μ ? ___

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

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

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

yes or no?

Answer 1

First enter Data into EXCEL

We have to find the sample mean.

Excel command is =AVERAGE(Select data)

sample mean = 16.43

n = 35

claim :premium rate justified for this client

a)

Null and alternative hypothesis is

Level of significance = 0.01

b)

Here population standard deviation is known so we use z-test statistic.

Test statistic is

Degrees of freedom = n - 1 = 35-1=34

c)

P-value =0.00776. ( using z table)

The P-Value is 0 .0078

P-value , Reject H0

d)

conclusion :Yes Using ? = .01, premium rate justified for this client.