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 49 orders using the new delivery process yields a sample mean of 27.7 minutes and a sample standard deviation of 6 minutes.

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? (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 ___________than the critical​ value, __________the null hypothesis and conclude that there is ___________evidence that the population mean 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 mean delivery time has been reduced below the previous population mean value of 30 minutes?

        What is the​ p-value for this​ test? (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 __________ than α _________the null hypothesis and conclude that there is ___________evidence that the population mean delivery time has been reduced below the previous population mean value of 30 minutes.

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

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

Answer 1

NULL HYPOTHESIS H0:

ALTERNATIVE HYPOTHESIS Ha:

alpha=0.05

t critical = -1.68

Since the test statistic is smaller than the critical​ value, REJECT the null hypothesis and conclude that there is Sufficient evidence that the population mean delivery time has been reduced below the previous population mean value of 30 minutes.

b) The P-Value is .005

Since the​ p-value is smaller than α ______REJECT___the null hypothesis and conclude that there is ______SUFFICIENT/ENOUGH_____evidence that the population mean delivery time has been reduced below the previous population mean value of 30 minutes.

c) Interpretation of P value:Small  P value indicates strong evidence against the null hypothesis.

d) Conclusion is same in both cases. First case used critical approach while second used P value approach.