Question

An advocacy group is interested in determining if gender (1 = Female, 2 = Male) affects executive level salaries. To this end, they took a random sample of executives in three different industries (1 = Consumer Goods, 2 = Financial, 3 = Health Care) and collected salary data. A partial two-way ANOVA table summarizing the results is provided below. Two-way ANOVA: Salary versus Industry, Gender Source MSF P Industry Gender Interaction Error Total DE SS 2 23342.6 1 4915.2 2 880.2 24 10794.0 29 39932.0 440.1 449.7 Boxplot of Salary 260 240 220 200 Salary 180 160 140 120 Gender Boxplot of Salary 260 240 220 200 Salary 180 160 140 120 Industry

Answer 1

Note: Final answers are highlighted in colour.

Question 29

The number of replications for the two way Anova procedure is:

Total samples= Total df+1=29+1=30

No of groups= 3 groups for Industry* 2 groups for gender= 6

Therefore ,No of replications=Total samples/No of groups= 30/6= 5 (Option 2)

Question 30

Null Hypothesis: Mean executive salaries are equal across industry sectors.(Option 2)

Question 31

In the current study, the experiment is just studying what is already existing. Researcher doesnt have any control over the variables(Gender, Industry). So this is an observational study.(Option 2)

Question 32

Standard Error= $\sqrt{\frac{SSE}{n-k}}$ = $\sqrt{\frac{10794}{30-6}}$ = 21.2073

Therefore Standard Error= 21.21(Option 2)

Question 33

F statistic for Gender

Mean square for Gender=Sum of Squares of Gender/df= 4915.2/1=4915.2

MSE= 449.7

F statistic= Mean square for Gender/MSE= 4915.2/449.7 =10.93

p value for F=10.93, degrees of freedom (1,29) is 0.002968

Therefore F statistic= 10.93, p- value= 0.003(Option 4)