Question

Please show all work (using a t-test), thank you.

2. You are the manager of a restaurant that delivers pizza to college dormitory rooms. You have just changed your delivery process in an effort to reduce the mean time between the order and the completion of delivery from the current 25 minutes. A sample of 36 orders using the new delivery process yields a sample mean of 22.4 minutes and a sample standard deviation of 6 minutes. What are the knowns in this problem in terms of sample and population data? At the 0.05 level of significance, test the hypothesis that the mean delivery time has been reduced below the previous population mean of 25 minutes. Step 1. What is the null and alternative hypothesis? Step 2. What is the test statistic from the sample? Step 3. What is/are the critical value(s) from the table? (Which table are you going to use?) Step 4. Based on the critical value(s), what are the rejections region(s)? Step 5-What comparison do you make to determine the conclusion to the hypothesis test in Step i? Step 6. What is your conclusion (reject or do not reject Ho)? State this in terms of the problem.

Answer 1

n = 36, x-bar = 22.4, s = 6, μ = 25

(a) Ho: μ ≥ 25 and Ha: μ < 25

(b) Test Statistic:    

SE = s/√n = 6/√36 = 1

t = (x-bar - μ)/SE = (22.4 - 25)/1 = -2.6

(c) Rejection Rule:    

α = 0.05   

Degrees of freedom = 36 - 1 = 35

Critical t- score = -1.68957244   

(d) Reject Ho if t < -1.68957244   

(e) Decision (in terms of the hypotheses):    

Since -2.6 < -1.68957244 we reject Ho and accept Ha

(f) Conclusion (in terms of the problem):    

There is sufficient evidence that the mean delivery time has reduced from the earlier 25 minutes.