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 85.7 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 102 2 67.9 56.3 75 4 80 0 956 86 3 70 7 64.6 810 E 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 95 Are the conditions for testing the hypothesis satisfied? V than the cntical value. In addition, a boxplot does not show any outliers AExpeted acore 2+ No, the conditions are not satisfied. The normal probability plot is not linear enough, since the correlation coefficient is greater less 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 = 857 *85 7 Find the test statistic Click to select your answer(s).
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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 85.7 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.
**[Table of Wait Times]**
- Order 1: 102.2 seconds
- Order 2: 67.9 seconds
- Order 3: 75.4 seconds
- Order 4: 64.6 seconds
- Order 5: 56.3 seconds
- Order 6: 85.2 seconds
- Order 7: 90.4 seconds
- Order 8: 89.9 seconds
- Order 9: 82.4 seconds
- Order 10: 81.0 seconds
(a) **Are the conditions for testing the hypothesis satisfied?**
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 \( r = 0.993 \).
- No, the conditions are not satisfied. The normal probability plot is [greater/less] (select the correct option) enough, since the correlation coefficient is [greater/less] (select the correct option) than the critical value. In addition, a boxplot does not show any outliers.
(b) **Is the new system effective? Conduct a hypothesis test using the P-value approach and a level of significance of \(\alpha = 0.01\)**
First determine the appropriate hypotheses:
\( H_0: \mu = 85.7 \)
\( H_1: \mu \neq 85.7 \)
Find the test statistic.
**Click to select your answer(s).**
**Graph Description:**
The image contains a normal probability plot titled "Expected z-score vs. Time (sec)" showing data points closely following a straight line, suggesting the data may be approximately normally distributed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F71553b3a-eb6b-4c59-80a6-2edc083690a2%2F19f86344-3e93-44a6-868a-df5c086543b8%2Frpc3y5n_processed.jpeg&w=3840&q=75)
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