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 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 30 minutes? State the null and alternative hypotheses for this test. O A. Ho: 230 Hu<30 OD. H: <30 HH230 OB. Horus 30 H:p>30 O E. H: 1527.7 HP> 27.7 OCHO:2 27.7 H: <27.7 OF. H: > 30 Hus 30 What is the test statistic for this test? STATO (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? 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 than 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. Choose the correct answer below. O A. 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 mean delivery time is 27.7 minutes. B. The p-value is the probability of selecting a sample of deliveries that has a mean delivery time of 27.7 minutes or more given that the population mean delivery time is 30 minutes O Click to select your answer(s).

Answer 1

null hypothesis: Alternate Hypothesis: 1.677 for 0.05 level with left tailed test and n-1=48 degree of freedom, critical value of t= Decision rule: reject Ho if test statistic t<-1.677 population mean sample mean sample size sample std deviation 30 27.700 49.00 5.000 standard error of mean = Sx=s/vn= 0.7143 t = (x-u)/sx= test statistic p value -3.220 0.0012

for hypothesis: option A is correct

tstat =-3.22

crtical value t = -1.68

since the test statistic is less than the critical value , reject the null,,,,there is sufficient evidenec,,,,,,,,,

b) p value =0.001

since the p value is less than alpha.reject the null,,,,there is sufficient evidenec,,,,,,,,,

c) .........mean delivery time of 27.7 minutes or less given that the population mean delivery time is 30