3. You are the manager of a restaurant that delivers pizza to college dormitory rooms. You have just

changed your delivery process in an effort to reduce the mean time between the order and completion

of delivery from the current 25 minutes. A sample of 36 orders using the new delivery process yields a

sample mean of 22.4 minutes and a sample standard deviation of 6 minutes.

Perform a hypothesis test to see whether there is evidence that the population mean delivery time has

been reduced below the previous population mean value of 25 minutes.

a. State your null hypothesis and alternative hypothesis.

b. Perform the test manually using critical value approach at the 0.05 level of significance.

c. What is your conclusion?

4. In industrial settings, alternative methods often exist for measuring variables of interest. The data in the

following table represent measurements in-linethat were collected from an analyzer during the

production process, and measurements from an analytical lab.

Perform a hypothesis test to see if there is evidence of a difference in the mean measurements in-line

and from an analytical lab.

Sample	In Line	Analytical Lab
1	8.01	8.01
2	7.56	7.29
3	7.47	7.54
4	7.4	7.42
5	7.83	7.8
6	7.5	7.65
7	6.86	6.93
8	7.31	7.46
9	7.45	7.6
10	7.23	7.4
11	7.37	7.5
12	7.49	7.41
13	6.21	6.25
14	6.68	6.54
15	5.12	5.2
16	4.84	4.7
17	4.84	4.82
18	5.21	5.33
19	5.35	5.3
20	5.6	5.4
21	5.32	5.39
22	5.16	5.17
23	5.66	5.5
24	6.31	6.24

a. State your null hypothesis and alternative hypothesis.

b. Perform the test manually using critical value approach at the 0.05 level of significance.

c. What is your conclusion?