A manager of a pizza restaurant has changed therestaurant's delivery process in an effort to reduce the mean time between the order and completion of delivery from the current 30 minutes. A sample of 36 orders using the new delivery process yields a sample mean of 27.8 minutes and a sample standard deviation of 5 minutes. Complete parts(a) through(d) below.

a. Using the critical valueapproach, at the 0.05 level ofsignificance, is there evidence that the population mean delivery time has been reduced below the previous population mean value of 30 minutes?

State the null and alternative hypotheses for this test.

A.

H0:>30

H1:30

B.

H0:27.8

H1:>27.8

C.

H0:30

H1:<30

Your answer is correct.

D.

H0:<30

H1:30

E.

H0:27.8

H1:<27.8

F.

H0:30

H1:>30

What is the test statistic for thistest?

tSTAT=

Whatis(are) the criticalvalue(s) for thistest?

What is the conclusion for thistest?

Since the test statistic is (1) than the criticalvalue, (2) the null hypothesis and conclude that there is (3) evidence that the population mean delivery time has been reduced below the previous population mean value of 30 minutes.

b. Using thep-value approach, at the 0.05 level ofsignificance, is there evidence that the population mean delivery time has been reduced below the previous population mean value of 30 minutes?

What is thep-value for thistest?

p-value=

What is the conclusion for thistest?

Since thep-value is (4) than , (5) the null hypothesis and conclude that there is (6) evidence that the population mean delivery time has been reduced below the previous population mean value of 30 minutes.

c. Interpret the meaning of thep-value in this problem. Choose the correct answer below.

A. Thep-value is the probability of selecting a sample of deliveries that has a mean delivery time of 27.8 minutes orless, given that the population mean delivery time is 30 minutes.

B. Thep-value is the probability of selecting a sample of deliveries that has a mean delivery time of 27.8 minutes ormore, given that the population mean delivery time is 30 minutes.

C. Thep-value is the probability of selecting a sample of deliveries that has a mean delivery time of 30 minutes ormore, given that the population mean delivery time is 27.8 minutes.

D. Thep-value is the probability of selecting a sample of deliveries that has a mean delivery time of 30 minutes orless, given that the population mean delivery time is 27.8 minutes.

d. Compare your conclusions in(a) and(b). Choose the correct answer below.

A. Using the critical valueapproach, the null hypothesis was rejected and using thep-value approach the null hypothesis was rejected. The critical value approach and thep-value approach are two different methods of finding the same answer.

B. Using the critical valueapproach, the null hypothesis was rejected and using thep-value approach, the null hypothesis was not rejected. The critical value approach and thep-value approach yield opposite results.

C. Using the critical valueapproach, the null hypothesis was not rejected and using thep-value approach, the null hypothesis was rejected. The critical value approach and thep-value approach yield opposite results.

D. Using the critical valueapproach, the null hypothesis was notrejected and using thep-value approach the null hypothesis was notrejected. The critical value approach and thep-value approach are two different methods of finding the same answer.

(1)less

greater

(2)reject

do not reject

(3)insufficient

sufficient

(4)less

greater

(5)reject

do not reject

(6)sufficient

insufficient