Question

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 27.3 minutes and a sample standard deviation of 6 minutes. Complete parts​ (a) through​ (d) below.

a. Using the critical value​ approach, at the 0.05 level of​ significance, 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

What is the test statistic for this​ test?

Use the information given above to determine whether or not to reject the null hypothesis.

b. Using the​ p-value approach, at the 0.01 level of​ significance, is there evidence that the population mean delivery time has been reduced below the previous population mean value of 30 ​minutes? f the​ p-value is less than the level of​ significance, reject H0. ​Otherwise, do not reject H0.

c. Interpret the meaning of the​ p-value in this problem.

d. Compare your conclusions in​ (a) and​ (b).

Examine the conclusions made in parts​ (a) and​ (b) above

Answer 1

Excel add-in (PH Stat) procedure: Step 1: In EXCEL, Select Add-Ins > PH Stat > One-Sample Tests > t Test for the mean, Sigma unknown. Step 2: Enter 30 under Null hypothesis. Step 3: Enter 0.05 under Level of significance. Step 4: In Sample Statistic Options, choose Sample Statistic Known and enter 36 as the Sample size and 27.3 as the Sample mean, and 6 as the Sample standard deviation. Step 5: In Test Options, choose Lower Tail Test. Step 6: Click OK Excel add-in (PH Stat) output:

t Test for Hypothesis of the Mean 0 Data Null Hypothesis = Level of significance 1 Sample Size Sample Mean Sample Standard Deviation 30 .05 36 27.3 6 Intermediate Calculations Standard Error of the Mean 1.0000 Degrees of Freedom 35 t Test Statistic -2.7000 Lower-Tail Test Lower Critical Value p-Value Reject the null hypothesis - 1.6896 0.0053 Test Statistic: t = -2.70. Critical value: tanie = -1.6896. Since teac (=-2.70) <tçrit(=-1.6896), then reject the null hypothesis.

Therefore, there is sufficient evidence that the population mean delivery time has been reduced below the previous population mean value of 30 minutes. (6) Since p-value (= 0.0053)s al=0.01), then reject the null hypothesis. Therefore, there is sufficient evidence that the population mean delivery time has been reduced below the previous population mean value of 30 minutes. (c) There is 0.53% of chance to support the null hypothesis is true. (d) The conclusions of (a) and (b) are same.