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 87 seconds. A manager devises a new drive-through system that she believes will decrease wait time. To test this, she initiates the new system at her 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.
(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 = 0.977. Are the conditions for testing the hypothesis satisfied? Yes, the conditions are satisfied. The normal probability plot is linear enough, since the correlation coefficient is greater than the critical value.
(b) Is the new system effective? Conduct a hypothesis test using the P-value approach and a level of significance of α = 0.01. First determine the appropriate hypotheses. Find the test statistic. Find the P-value. Use the α = 0.01 level of significance. What can be concluded from the hypotheses? The P-value is greater than the level of significance, so there is not sufficient evidence to conclude that the new system is effective.