Question

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 at least 25 minutes. A sample of 36 orders using the new delivery process yields a sample mean of 23.8 minutes and a sample standard deviation of 6 minutes. At the 0.05 level of significance, is there evidence that the population mean delivery time has been reduced below 25 minutes? Which of the following are the appropriate null and alternative hypotheses?

• A. H0: μ <= 25 vs. H1: μ > 25
• B. H0: μ > 25 vs. H1: μ < 25
• C. H0: μ = 25 vs. H1: μ ≠ 25
• D. H0: μ >= 25 vs. H1: μ < 25

Answer 1

The null and alternate hypothesis are:
H0:
Ha:

Hence option D is the correct option.

The test statistic value is given by:

Since this is a left-tailed test, so the p-value is given by:

Since p-value is greater than 0.05, so we do not have sufficient evidence to reject the null hypothesis H0. Thus we say that i.e. the delivery time is greater than or equal to 25.