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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 86.4 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.
Data:
105.8
68.8
58.4
76.3
67.9
81.3
94.1
84.1
72.3
81.0
(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 and boxplot are shown. 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=0.01.
H0:
H1:
Find the test statistic:
Find the P value:
What can be concluded from the hypothesis test?
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