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 87.4 seconds. A manager 104.1 82.6 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 69.0 93.5 for 10 randomly selected orders. The wait times are provided in the table to the right. Complete parts (a) and (b) below. 58.2 85.6 74.6 71.4 67.6 83.4 (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 = 0.987. Are the conditions for testing the hypothesis satisfied? the conditions satisfied. The normal probability plot linear enough, since the correlation coefficient is than the critical value. In A Expected z-score 2- addition, a boxplot does not show any outliers. 60 5 90 105 Time (sec) (b) Is the new system effective? Conduct a hypothesis test using the P-value approach and a level of significance of a = 0.01. First determine the appropriate hypotheses. X Ho 87.4 Critical values Hy: V 87.4 Find the test statistic. Sample Size, n Critical Value Sample Size, n Critical Value 5 0.880 16 0.941 to =] 6 0.888 17 0.944 7 0.898 18 0.946 (Round to two decimal places as needed.) 8 0.906 19 0.949 Find the P-value. 9 0.912 20 0.951 10 0.918 21 0.952 The P-value is 11 0.923 22 0.954 (Round to three decimal places as needed.) 12 0.928 23 0.956 13 0.932 24 0.957 14 0.935 25 0.959 15 0.939 30 0.960