Question

The mean waiting time at the​ drive-through of a​ fast-food restaurant from the time an order is placed to the time the order is received is 85.8 seconds. A manager devises a new​drive-through system that he believes will decrease wait time. As a​ test, he initiates the new system at his restaurant and measures the wait time for 10 randomly selected orders. The wait times are provided in the table to the right. Complete parts​ (a) and​ (b) below.

101.1
66.8
57.0
75.0
64.4
81.0
94.7
87.8
72.3
79.9

a) Because the sample size is​ small, the manager must verify that the wait time is normally distributed and the sample does not contain any outliers. The normal probability plot is shown below and the sample correlation coefficient is known to be r=0.995 Are the conditions for testing the hypothesis​ satisfied?

b) Is the new system​ effective? Conduct a hypothesis test using the​ P-value approach and a level of significance of α=0.05. First determine the appropriate hypotheses. Find the t- statistic? Find the P Value? Conclude the hypothesis.

Answer 1