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 87.887.8 seconds. A manager devises a new​ drive-through system that hehe believes will decrease wait time. As a​ test, hehe initiates the new system at hishis restaurant and measures the wait time for 1010 randomly selected orders. The wait times are provided in the table to the right. Complete parts​ (a) and​ (b) below. 102.6102.6 80.080.0

68.468.4 96.996.9 57.057.0 87.287.2 76.476.4 71.271.2 64.264.2 86.186.1 LOADING... Click the icon to view the table of correlation coefficient critical values. Question content area bottom Part 1 ​(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 requals=0.9940.994. 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. In​ addition, a boxplot does not show any outliers. 60 75 90 105 -2 -1 0 1 2 Time (sec) Expected z-score

A normal probability plot has a horizontal axis labeled Time (seconds) from 50 to 115 in increments of 5 and a vertical axis labeled Expected z-score from negative 2 to 2 in increments of 0.5. Ten plotted points closely follow the pattern of a line that rises from left to right through (57, negative 1.55) and (97, 1). All coordinates are approximate. Part 2 ​(b) Is the new system​ effective? Conduct a hypothesis test using the​ P-value approach and a level of significance of alpha equals 0.1α=0.1. First determine the appropriate hypotheses. Upper H 0H0​: muμ equals= 87.887.8 Upper H 1H1​: muμ less than< 87.887.8 Part 3 Find the test statistic. t 0t0equals=negative 1.93−1.93 ​(Round to two decimal places as​ needed.) Part 4 Find the​ P-value. The​ P-value is