In: Statistics and Probability
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 25 minutes. A sample of 36 orders using the new delivery process yields a sample mean of 22.1 minutes and a sample standard deviation of 5 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 25 minutes?
State the null and alternative hypotheses for this test.
What is the test statistic for this test?
What is(are) the critical value(s) for this test?
What is the conclusion for this test?
b. Using the p-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 25 minutes?
What is the p-value for this test?
What is the conclusion for this test?
c. Interpret the meaning of the p-value in this problem.