A regional manager wants to know if there is a difference between the mean amounts of time that customers wait in line at the drive-through window for the three stores in her region. She randomly samples the wait times at each store. Her data are given in the following table. Use a one-way ANOVA test to determine if there is a difference between the mean wait times for the three stores, at the 0.01 level of significance. Assume the population distributions are approximately normal with equal population variances. \begin{tabular}{|c|c|c|} \hline \multicolumn{3}{|c|}{ Drive-Through Wait Times (in Minutes) } \\ \hline Store 1 & Store 2 & Store 3 \\ \hline 2.49 & 3.33 & 2.78 \\ \hline 2.78 & 3.24 & 2.59 \\ \hline 2.88 & 2.74 & 2.95 \\ \hline 2.94 & 2.95 & 3.01 \\ \hline 2.74 & 2.83 & 3.24 \\ \hline 2.72 & 3.16 & 2.59 \\ \hline 2.56 & 3.03 & 2.72 \\ \hline \end{tabular} Copy Data Step 1 of 2: Compute the value of the test statistic. Round any intermediate calculations to at least six decimal places, and round your final answer to four decimal places. Answer Tables Keypad Keyboard Shortcuts \[ F= \]
Solution
Step 1 ：First, we store the wait times for each store in separate arrays. For Store 1, the wait times are [2.49, 2.78, 2.88, 2.94, 2.74, 2.72, 2.56]. For Store 2, the wait times are [3.33, 3.24, 2.74, 2.95, 2.83, 3.16, 3.03]. For Store 3, the wait times are [2.78, 2.59, 2.95, 3.01, 3.24, 2.59, 2.72].
Step 2 ：Next, we perform a one-way ANOVA test on the wait times. The one-way ANOVA test is used to determine whether there are any statistically significant differences between the means of three or more independent groups.
Step 3 ：The result of the one-way ANOVA test is an F-value, which represents the ratio of the between-group variability to the within-group variability. A larger F-value indicates a larger difference between the groups relative to the variability within the groups.
Step 4 ：The F-value for the one-way ANOVA test is calculated to be 3.7113. This value is rounded to four decimal places as requested in the question.
Step 5 ：Finally, we conclude that the F-value for the one-way ANOVA test is \(\boxed{3.7113}\). This value represents the ratio of the between-group variability to the within-group variability. A larger F-value indicates a larger difference between the groups relative to the variability within the groups. However, to determine whether this difference is statistically significant, we would need to compare the F-value to a critical value or calculate a p-value. This was not requested in the question, so we stop here.
