Question

You are hired to do some data analysis for a financial services company. There are three different Investment Plans that the company could offer to its customers. You are asked to find out if the expected revenue from marketing any one of these plans is different from the other plans. You survey 60 customers and this survey asks each customer to choose a plan they prefer and also involves other relevant questions that allow you to compute the expected revenues that the company can generate from each customer. Given the three different plans and the expected revenues, test whether each plan generates the same mean revenue. If the mean revenue generated is different depending on the marketed plan, which plan would be a better choice?      

Inv Revenue

1   4500.00
1   1100.00
1   3500.00
1   3000.00
1   2750.00
1   2800.00
1   2400.00
1   2100.00
1   5200.00
1   4250.00
1   3500.00
1   3000.00
1   2750.00
1   1600.00
1   2400.00
1   1300.00
1   5900.00
1   4500.00
1   4250.00
1   3500.00
2   4500.00
2   5000.00
2   3500.00
2   5450.00
2   6200.00
2   5750.00
2   7500.00
2   8000.00
2   8450.00
2   4500.00
2   5000.00
2   3500.00
2   5450.00
2   6200.00
2   5750.00
2   7500.00
2   8000.00
2   8450.00
2   8900.00
2   5000.00
3   6000.00
3   7000.00
3   8500.00
3   9250.00
3   9450.00
3   9900.00
3   10000.00
3   11000.00
3   5000.00
3   6000.00
3   7000.00
3   8500.00
3   9250.00
3   9450.00
3   9900.00
3   10000.00
3   11000.00
3   6500.00
3   6540.00
3   7100.00

Answer 1

One-way ANOVA: Revenue versus Inv

Method

Null hypothesis	All means are equal
Alternative hypothesis	Not all means are equal
Significance level	α = 0.05

Equal variances were assumed for the analysis.

Factor Information

Factor	Levels	Values
Inv	3	1, 2, 3

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Inv	2	266963320	133481660	51.83	0.000
Error	57	146790320	2575269
Total	59	413753640

Since p-value is less than alpha 0.05, we reject null hypothesis and there is a significant evidence to conclude that the mean revenue generated is different depending on the marketed plan

Tukey Pairwise Comparisons

Tukey Simultaneous Tests for Differences of Means

Difference of Levels	Difference of Means	SE of Difference	95% CI	T-Value	Adjusted P-Value
2 - 1	2915	507	(1695, 4135)	5.74	0.000
3 - 1	5152	507	(3932, 6372)	10.15	0.000
3 - 2	2237	507	(1017, 3457)	4.41	0.000

All the three comparisons 2-1, 3-1 and 3-2 are significantly different and since the difference is highest in case of 3-1 comparison and it is positive we conclude that plan 3 would be a better choice.