7. Consider the following hypothetical outcome of a two-way factorial designs [8 points]

Pink/Car Pink/Bike Blue/Car Blue/Bike
58 56 70 21
45 96 69 25
61 88 28 31
59 78 53 23
23 59 65 79
19 65 20 17
48 41 51 18
33 22 69 28
65 46 87 35
27 10 39 20
38 17 75 29
42 29 96 24
66 19 28 44
50 54 58 26
54 69 71 30

a. Calculate the marginal means for each factor (show the numbers that go into each mean).

b. Draw an interaction line graph (label each point with its numerical value),

a. To calculate the marginal means for each factor, we need to find the mean for each level of the factor while ignoring the other factor.

For the "Pink/Car" factor:

Mean of Pink/Car = (58 + 45 + 61 + 59 + 23 + 19 + 48 + 33 + 65 + 27 + 38 + 42 + 66 + 50 + 54) / 15
= 757 / 15
= 50.47

For the "Pink/Bike" factor:

Mean of Pink/Bike = (56 + 96 + 88 + 78 + 59 + 65 + 41 + 22 + 46 + 10 + 17 + 29 + 19 + 54 + 69) / 15
= 836 / 15
= 55.73

For the "Blue/Car" factor:

Mean of Blue/Car = (70 + 69 + 28 + 53 + 65 + 20 + 51 + 69 + 87 + 39 + 75 + 96 + 28 + 58 + 71) / 15
= 908 / 15
= 60.53

For the "Blue/Bike" factor:

Mean of Blue/Bike = (21 + 25 + 31 + 23 + 79 + 17 + 18 + 28 + 35 + 20 + 29 + 24 + 44 + 26 + 30) / 15
= 415 / 15
= 27.67

b. To draw an interaction line graph, we need to plot the mean values for each combination of the two factors.

First, we plot the mean values for the Pink/Car factor: (Pink/Car, Mean)
(1, 50.47)
(2, 55.73)

Next, we plot the mean values for the Blue/Car factor: (Blue/Car, Mean)
(1, 60.53)
(2, 27.67)

Finally, we connect the points with lines and label each point with its numerical value.

The graph will have two lines, one for the Pink/Car factor and one for the Blue/Car factor. The x-axis will represent the different levels of the factors (1 and 2), and the y-axis will represent the mean value for each combination.

Note: Since we do not have the full data set, we cannot provide an actual visualization of the graph.