The waiting time to place an order at a branch of a fast-food chain during the lunch hour has had population mean of 3.55 minutes, with a population standard deviation of 1.1 minute. Recently, in an effort to reduce the waiting time, the branch has experimented with a system in which there is a single waiting line. A sample of 100 customers during a recent lunch hour was selected, and their mean waiting time to place an order was 3.18 minutes. Assume that the population standard deviation of the waiting time has not changed from 1.1 minutes.
a. At the 0.05 level of significance, using the critical value approach to hypothesis testing, is there evidence that the population mean waiting time to place an order is less than 3.55 minutes?
b. At the 0.05 level of significance, using the p-value approach to hypothesis testing, is there evidence that the population mean waiting time to place an order is less than 3.55 minutes?
c. Interpret the meaning of the p-value in this problem.
d. Compare your conclusion in (a) and (b).
This solution conducts a statistical analysis on the mean waiting times at a fast-food chain by presenting the null and alternative hypothesis, calculating the test statistic and comparing it to the p-value. A decision is made to accept or reject the null hypothesis. It also explains the p-value and compares the two hypothesis testing conditions.