Mart A sells bread. It is implicated that the area of bread display and the height of the displayed shelf could affect the bread sales. The shelf height (top, middle, bottom) and display area (large, small) were varied, and in a total of 6 cases, the number of bread sold during the day was repeated twice and observed.

	Large	Small
Top	30 28	31 35
Middle	57 51	56 60
Bottom	36 32	35 29

(1) Find the average of the observation values of 6 cells, and graph the change in the average value according to the shelf height (top, middle, bottom) for each display area (large and small). Do you think there is an interaction between the shelf height effect and the display area effect?

(2) Accurately describe the model and assumptions of the binary placement method with repetition, and make an appropriate hypothesis as to whether each effect is significant.

(3) Prepare the following ANOVA table, test the hypothesis of (2) at the significance level of 5%, and interpret the results. Are the results on the significance of the interaction consistent with the prediction in (1)? If there are no interactions, test the main effects in the new model. (rounded to 4 decimal places)

Factor	Sum of Squares	Degrees of Freedom	Mean Square	F Value	Rejection
Factor A
Factor B	1544
Interaction
Residual	62
Total	1642	11