Question

4. What affects marketing managers' hourly wages? In order to find out, hourly wages were found for two managerial occupations in marketing (Sales and Advertising) for a random sample of US States from three geographic regions (Midwest, Southwest and West). A two-factor balanced design is used with three obses- vations per each combination of level of managerial occupation with geographic region. (a) Identify the response variable, factors and their levels (b) Define the parameters being tested for. (c) Explain why there might be interaction bet ween the factors of the study. (d) Clearly state null and alternative hypotheses (e) Here is an incomplete ANOVA table: df SS MS 1326 154 Source Manager Type Region Interaction Error Total 42 Find the F-ratios and associated P-values. (f) State your conclusions.

Answer 1

(a) response variable is the hourly wages of managerial occupation in marketing.

Two factors are sales and advertising

Three levels are three geographical regions midwest, southwest and west.

(b) Parameters being tested are

main effects :

(i)Manager type (ii)  Region

interaction effect :

Manager type * Region

(c) The average change in response across the levels of one factor may not be same at all the levels of other factor , so interaction effect is present.

(d) The null hypotheses

H0: Main effect (Manager type) has no significant effect on the design.

H0: Main effect (Region) has no significant effect on the design.

H0: There is no significant interaction between Manager type and Region.

The alternative hypotheses

Ha: Main effect (Manager type) has significant effect on the design.

Ha: Main effect (Region) has significant effect on the design.

Ha: There is significant interaction between Manager type and Region.

(e) Total number of observation = 2*3*3 = 18

Source	df	SS	MS	F	P value
Manager type	2-1=1	1326	1326	378.85	<0.0001(significant)
Region	3-1=2	154	771	220.29	<0.0001(significant)
Interaction	(2-1)*(3-1)=2	33	16.5	4.71	0.0309(significant)
Error	2*3*(3-1)=12	42	3.5
Total	18-1=17

Note : MS = SS/df

F(region)= MS(region)/ MS(error)

(f) Since P value < 0.05

There is sufficient evidence at 0.05 level to conclude that

Main effect (Manager type) has significant effect on the design.

Main effect (Region) has significant effect on the design.

There is significant interaction between Manager type and Region.