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 87.6 seconds. A manager devises a new drive-through system...

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 87.6 seconds. A manager devises a new​ drive-through system that she believes will decrease wait time. As a​ test, 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.

Extracted text: 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 87.6 seconds. A manager devises a new drive-through system that she believes will decrease wait time. As a test, 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. 108.4 79.9 67.9 93.8 58.4 85.7 76.0 69.9 65.2 84.8 Click the icon to view the table of correlation coefficient critical values. (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= 0.982. Are the conditions for testing the hypothesis satisfied? satisfied. The normal probability plot than the critical value. In addition, a boxplot does not show any outliers. AExpected Z-score 2- the conditions linear enough, since the correlation coefficient is 1 0- 60 75 90 105 -1- -2- Time (sec) (b) Is the new system effective? Conduct a hypothesis test using the P-value approach and a level of significance of a = 0.05. First determine the appropriate hypotheses. Ho: 87.6 H4: 87.6 Find the test statistic. to = (Round to two decimal places as needed.) Find the P-value. The P-value is (Round to three decimal places as needed.)