QuestionMara Stratton
12/03/24 6:28 PM
Question 6, 10.3.21-T
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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 86.8 seconds. A manager 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 for 10 randomly selected orders. The wait times are provided in the table to the right. Complete parts (a) and (b) below.
\begin{tabular}{|c|c|}
\hline 105.8 & 82.9 \\
66.1 & 96.3 \\
59.6 & 85.3 \\
76.2 & 72.3 \\
65.2 & 80.3 \\
\hline
\end{tabular}
Click the icon to view the table of correlation coefficient critical values.
(b) Is the new system effective? Conduct a hypothesis test using the P -value approach and a level of significance of .
First determine the appropriate hypotheses.
Find the test statistic.
(Round to two decimal places as needed.)
Find the P -value.
The -value is .
(Round to three decimal places as needed.)
Time (sec)
3
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STEP 1
1. The mean waiting time under the old system is seconds.
2. The sample size is .
3. The sample mean and standard deviation need to be calculated from the given data.
4. The significance level is .
5. The hypothesis test is two-tailed.
STEP 2
1. State the hypotheses.
2. Calculate the sample mean and standard deviation.
3. Calculate the test statistic.
4. Find the P-value.
5. Make a decision based on the P-value.
STEP 3
State the null and alternative hypotheses:
STEP 4
Calculate the sample mean () and sample standard deviation () from the data:
Data:
Calculate :
Calculate using the formula for sample standard deviation.
STEP 5
Calculate the sample mean:
Calculate the sample standard deviation :
Calculate the deviations and sum of squares.
STEP 6
Calculate the test statistic :
Given .
STEP 7
Find the P-value for the test statistic using a t-distribution with degrees of freedom.
Use a t-table or statistical software to find the P-value.
STEP 8
Compare the P-value to the significance level .
If -value < , reject the null hypothesis .
The P-value is approximately .
Since , we do not reject the null hypothesis.
Conclusion: There is not enough evidence to suggest that the new system is effective at reducing the mean wait time.
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