Question

A consumer organization studied the effect of age and gender of automobile owners on size of cash offer for a used car by utilizing 6 men and 6 women in each of three age groups (young, middle, elderly) who acted as the owner of a used car. A medium price six-year-old car was selected for the experiment, and the owners solicited cash offers for this car from 36 dealers selected at random from the dealers in the region. Randomization was used in assigning dealers to the owners. The offers (in hundred dollars) were recorded in the data. Consider Factor A = age and Factor B = gender.

1. [1 pt] Write the ANOVA model.

2. [2.0 pts] Check the assumptions of the ANOVA model you considered.

3. [0.5 pt]Propose and display graphs showing the main effects and interaction effects. What do you conclude?

4. [0.5 pt] Test whether interaction effects are present; use a = 0.05. Is it meaningful here to test for the main factor effects? Explain.

5. [1 pt] Test whether age and gender main effects are present using a = 0.05.

Please solve the question by using SPSS and write the steps in SPSS to solve this problem.

Question Data:

Offer	Age	Gender
21.00	1	1
23.00	1	1
19.00	1	1
22.00	1	1
22.00	1	1
23.00	1	1
21.00	1	2
22.00	1	2
20.00	1	2
21.00	1	2
19.00	1	2
25.00	1	2
30.00	2	1
29.00	2	1
26.00	2	1
28.00	2	1
27.00	2	1
27.00	2	1
26.00	2	2
29.00	2	2
27.00	2	2
28.00	2	2
27.00	2	2
29.00	2	2
25.00	3	1
22.00	3	1
23.00	3	1
21.00	3	1
22.00	3	1
21.00	3	1
23.00	3	2
19.00	3	2
20.00	3	2
21.00	3	2
20.00	3	2
20.00	3	2

Answer 1

a)

The two way ANOVA model with interaction is

i=1,2

j=1,2,3

k=1,2,...,n_ij

Assumption, e_ijk ~ N(0,)

b)

The normal probability plot is

Hence the data is normal with 99% confidence.

we have run this in R to get the equal variance test for each group of age and gender

the output is

hence we can say that the all group has same mean since each has p-value > 0.05

c)

We have done interaction plot in R and get the output as

so we can say there is no interaction between age and gender as two are not intersecting.

d)

Test whether interaction effects are present; use a = 0.05. Is it meaningful here to test for the main factor effects? Explain.

We will construct ANOVA table for this

since p-value corresponding interaction is 0.36>0.05 we can say that there is no interaction between age and gender.

Test whether age and gender main effects are present using a = 0.05.

only age has p-value<0.05 we can say that the age is significant and gender is insignificant.