Question

4. An airline wants to know the impact of method of redeeming frequent-flyer miles and the age group of customers on how the number of miles they redeemed. To do so, they perform a two-way analysis of variance on the data for miles redeemed shown on cells L35 to O43 on the answers sheet.
	a. Identify the null and alternative hypotheses for each of the two main effects and the interaction.
	b. Use two-way analysis of variance to test each of these three sets of hypotheses at the 0.05 significance level.

	Customer age ranges
Methods of redeeming miles	Under 25	25 to 40	41 to 60	Over 60
Cash	300,000	60,000	40,000	0
	0	0	25,000	5,000
	25,000	0	25,000	25,000
Discount Vacations	40,000	40,000	25,000	45,000
	25,000	25,000	50,000	25,000
	0	5,000	0	0
Discount Internet Shopping Spree	25,000	30,000	25,000	30,000
	25,000	25,000	50,000	25,000
	75,000	50,000	0	25,000

b.	SS	df	MS	Fcalc	Fcrit				p-value
Methods of redeeming miles						Reject H0or not?				α =	0.05
Customer age ranges						Reject H0or not?				α =	0.05
Interaction						Reject H0or not?				α =	0.05
Error

Answer 1

Hypothesis 1

H0 : The mean number of miles redeemed is the same across age groups
H1 : The mean number of miles redeemed is not the same across age groups

Hypothesis 2
H0 : The mean number of miles redeemed is the same for all the three methods of redeeming miles
H1 : The mean number of miles redeemed is not the same for all the three methods of redeeming miles

Hypothesis 3

H0 : There in no interaction between the age group and the method of redeeming.
H1: There in an interaction between the age group and the method of redeeming.

2 ways anova in excel.

1. Input the data in excel as shown

2. Under the data tab, select the data analysis and select two way anova with replication.

3. Update the input in the dialogue box

4. The output is generated as follows.

We use the pvalue for testing the hypothesis. (Highlighted in yellow).
Also the next to the anova output is have indicated which pvalue correspond to which variable.

Methods of redeeming miles
Here the pvalue 0.65 is greater than 0.05, hence we fail to reject the null hypothesis and conclude that the mean number of miles redeemed is the same for all the three methods of redeeming miles

Age group
Here the pvalue 0.74 is greater than 0.05, hence we fail to reject the null hypothesis and conclude that the mean number of miles redeemed is the same for all the three methods of redeeming miles

Interaction
Here the pvalue 0.85 is greater than 0.05, hence we fail to reject the null hypothesis and conclude that there in no interaction between the age group and the method of redeeming.