A manager of a pizza restaurant has changed the restaurant'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 27.4 minutes and a sample standard deviation of 5 minutes.

a. Using the critical value approach, at the 0.05 level of significance, is there evidence that the population means the delivery time has been reduced below the previous population means the value of 30 minutes? State the null and alternative hypotheses for this test.

H0: 27.4

H1: <27.4

H0: 30

H1: >30

H0: 27.4

H1: >27.4

H0: >30

H1: 30

H0: <30

H1: 30

H0: 30

H1: <30

What is the test statistic for this test?

tSTAT = _____

(Type an integer or a decimal. Round to two decimal places as needed.)

What is(are) the critical value(s) for this test?

______

(Type an integer or a decimal. Round to two decimal places as needed. Use commas to separate your answers as needed.)

What is the conclusion for this test?

Since the test statistic is (less, greater, than the critical value), (do not reject, reject, the null hypothesis and conclude that there is) (sufficient, insufficient) evidence that the population means the delivery time has been reduced below the previous population mean value of 30 minutes.

b. Using the p-value approach, at the 0.05 level of significance, is there evidence that the population means the delivery time has been reduced below the previous population means the value of 30 minutes? What is the p-value for this test? P-value = _____

(Type an integer or a decimal. Round to three decimal places as needed.)

What is the conclusion for this test?

Since the p-value is (less than a, greater than ) (do not reject, reject, the null hypothesis and conclude that there is) (sufficient, insufficient) evidence that the population means the delivery time has been reduced below the previous population means value of 30 minutes.

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

1. The p-value is the probability of selecting a sample of deliveries that has a mean delivery time of 27.4 minutes or more, given that the population means delivery time is 30 minutes.
2. The p-value is the probability of selecting a sample of deliveries that has a mean delivery time of 27.4 minutes or less, given that the populations means delivery time is 30 minutes.
3. The p-value is the probability of selecting a sample of deliveries that has a mean delivery time of 30 minutes or less, given that the population means delivery time is 27.4 minutes.
4. The p-value is the probability of selecting a sample of deliveries that has a mean delivery time of 30 minutes or more, given that the population means delivery time is 27.4 minutes.

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

1. Using the critical value approach, the null hypothesis was rejected, and using the p-value approach the null hypothesis was rejected. The critical value approach and the p-value approach are two different methods of finding the same answer.
2. Using the critical value approach, the null hypothesis was not rejected, and using the p-value approach, the null hypothesis was rejected. The critical value approach and the p-value approach yield opposite results.
3. Using the critical value approach, the null hypothesis was rejected, and using the p-value approach, the null hypothesis was not rejected. The critical value approach and the p-value approach yield opposite results.
4. Using the critical value approach, the null hypothesis was not rejected, and using the p-value approach the null hypothesis was not rejected. The critical value approach and the p-value approach are two different methods of finding the same answer.