Suppose that I am the efficiency-control manager at a fast-food restaurant. Part of my job is to determine how long it takes to get orders to our customers. I want to know whether our efficiency changes across all 100 of our restaurants over a 6-month period. I collect data to figure out the average length of time it takes to get orders to customers at the beginning of the 6-month period, three months into the study period, and at the end of the 6-month period. I get the following data (in seconds per order):
$\begin{array}{lccc}& \text {Beginning of 6 } &\text { 3 months into study } &\text { End of 6 -months months } \\&\text {months } \\\hline \text { Seconds per order } & 120 & 150 & \\\\\hline\end{array}$
a. Create a line graph to represent the data presented in the table above.
b. Interpret this graph. What does it tell you?
c. Now that I have seen my results and they suggest that we got slower in the middle of the study, I want to know whether this slow-down was consistent across the different regions where we have restaurants. So suppose I divide the restaurants into those in the east coast of the United States and those on the west coast. I get the following results:
$\begin{array}{lccc}& \text {Beginning of 6} &\text {3 months into study } &\text { End of 6-months months } \\&\text { months } \\\hline \text { Seconds per order in } & 125& 180& 110 \\ \text { the East } \\\\ \text { Seconds per order in } & 115& 120& 120 \\ \text { the West } \\\hline\end{array}$
Create a line graph of these means.
d. What is the between-subjects variable in this mixed-model ANOVA?
e. Looking at the data presented in the table and figure above, do you think there is a time X region interaction on the dependent variable?
f. Suppose that the ANOVA results produced a value for the interaction between Time of Assessment and Seconds per order of F_(2,98)= 4.36. Using an alpha level of .05, is this a statistically significant interaction?

Question

Suppose that I am the efficiency-control manager at a fast-food restaurant. Part of my job is to determine how long it takes to get orders to our customers. I want to know whether our efficiency changes across all 100 of our restaurants over a 6-month period. I collect data to figure out the average length of time it takes to get orders to customers at the beginning of the 6-month period, three months into the study period, and at the end of the 6-month period. I get the following data (in seconds per order):

\begin{array}{lccc}& \text {Beginning of 6 } &\text { 3 months into study } &\text { End of 6 -months months } \\&\text {months } \\\hline \text { Seconds per order } & 120 & 150 & \\\\\hline\end{array}

a. Create a line graph to represent the data presented in the table above.
b. Interpret this graph. What does it tell you?
c. Now that I have seen my results and they suggest that we got slower in the middle of the study, I want to know whether this slow-down was consistent across the different regions where we have restaurants. So suppose I divide the restaurants into those in the east coast of the United States and those on the west coast. I get the following results:

\begin{array}{lccc}& \text {Beginning of 6} &\text {3 months into study } &\text { End of 6-months months } \\&\text { months } \\\hline \text { Seconds per order in } & 125& 180& 110 \\ \text { the East } \\\\ \text { Seconds per order in } & 115& 120& 120 \\ \text { the West } \\\hline\end{array}

Create a line graph of these means.
d. What is the between-subjects variable in this mixed-model ANOVA?
e. Looking at the data presented in the table and figure above, do you think there is a time X region interaction on the dependent variable?
f. Suppose that the ANOVA results produced a value for the interaction between Time of Assessment and Seconds per order of F_(2,98)= 4.36. Using an alpha level of .05, is this a statistically significant interaction?

Quizplus · Accepted Answer

The Answer is a.

a. b. It appears that, on average across the 100 restaurants, it took longer to deliver orders to customers in the middle of the 6-month period of this study than it did at the beginning or the end. We would need to calulate the F value to determine whether this difference across the three time points is statistically significant. c. d. Region of the country that the restaurants were in. e. The seconds-per-order in the West remained relatively flat across the three times of data collection, but in the East the seconds-per-order was higher in the second data-collection point than it was in the first or last data collection point. f. Looking in Appendix C, with 2 and 100 degrees of freedom, the critical F value is 3.09. Because this critical F value is smaller than our observed F value of 4.36, we would conclude that this is a statistically significant interaction.

b. It appears that, on average across the 100 restaurants, it took longer to deliver orders to customers in the middle of the 6-month period of this study than it did at the beginning or the end. We would need to calulate the F value to determine whether this difference across the three time points is statistically significant.
c.

d. Region of the country that the restaurants were in.
e. The seconds-per-order in the West remained relatively flat across the three times of data collection, but in the East the seconds-per-order was higher in the second data-collection point than it was in the first or last data collection point.
f. Looking in Appendix C, with 2 and 100 degrees of freedom, the critical F value is 3.09. Because this critical F value is smaller than our observed F value of 4.36, we would conclude that this is a statistically significant interaction.

Suppose That I Am the Efficiency-Control Manager at a Fast-Food