A sporting goods retailer chain has stores with different store layouts and diff
ID: 3270232 • Letter: A
Question
A sporting goods retailer chain has stores with different store layouts and different management styles. Sales data have been collected on randomly selected stores in order to determine which layout and management style result in the best sales. Partial results of a two-way ANOVA are below (=0.05).
1. How many levels are there for Factor A (Store Layout)?
a. 2
b. 3
c.
4
d.
5
e.
6
2. How many levels are there for factor B (Management Style)?
a.
2
b.
3
c.
4
d.
5
e.
6
3. What is the Fcalc for Factor A (Store Layout)?
a.
10.97
b.
2.96
c.
3.71
d.
2.61
e.
2.13
4. What is the Fcalc value for the interaction term?
a. 1.36
b. 4.03
c.
2.98
d.
3.39
e.
3.79
c.
4
d.
5
e.
6
Sum of Squares Degrees of Freedom Mean Square 2004.7 5717.2 2 Store Layout (A) Management Style (B) Interaction 5717.2 6180.4 Total 555120.5 708Explanation / Answer
The two independent variables in a two-way ANOVA are called factors. The idea is that there are two variables, factors, which affect the dependent variable. Each factor will have two or more levels within it, and the degrees of freedom for each factor is one less than the number of levels.
1) 3...Option B
2) 2...Option A
3) Sum of squares for store layout :
SS/df = MS
SS = 2004.7 * 2 = 4009.4
So, SS for Error = 555120.5 - 4009.4 - 5717.2 - 6180.4 = 539213.5
MS = SS/df for error = 539213.5/703 = 767.02
F value for store = 2004.7/767.02 = 2.61....D option
4) MS for interaction = SS/df = 6180.4/2 = 3090.2
F value = 3090.2/767.02 = 4.03.... B option
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