Question

Divide the data into three groups according to age: under 25, 26 to 49, and over 50.

Use ANOVA to test the claim that all three of these groups have the same mean balance on their Visa card.

Be sure to write down the mean and standard deviation for each group!

Age <25                                26-49                                      over 50

n =                                          n =                                          n =

               

x =                                           x =                                         x =

s =                                          s =                                          s =

The data collected below comes from people that live in Salinas. Listed below are the genders, ages and current balance on one specific type of Visa card.

Gender	Balance	Age
M	235	19
M	122	24
M	1752	55
M	1543	62
M	1655	34
M	0	19
M	84	22
M	355	26
M	299	28
M	2404	45
M	848	54
M	667	71
M	1248	32
M	7746	38
M	0	41
M	8329	51
M	486	34
M	554	38
M	874	54
F	601	62
F	56	80
F	472	27
F	59	18
F	4233	49
F	2544	58
F	109	22
F	235	24
F	644	36
F	3484	57
F	1509	27
F	624	30
F	3324	59
F	2268	33
F	495	19
F	0	26

Answer 1

The hypothesis being tested is:

H₀: µ₁ = µ₂ = µ₃

H_a: Not all means are equal

Age < 25	26-49	over 50
19	34	55
24	26	62
19	28	54
22	45	71
27	32	51
18	38	54
22	41	62
24	34	80
19	38	58
	49	57
	36	59
	27
	30
	33
	26
n = 9	n = 15	n = 11
x = 21.6	x = 34.5	x = 60.3
s = 3.05	s = 6.88	s = 8.49
	21.6	9	3.05	Age < 25
	34.5	15	6.88	26-49
	60.3	11	8.49	over 50
	39.3	35	16.70	Total
ANOVA table
Source	SS	df	MS	F	p-value
Treatment	8,022.55	2	4,011.274	88.15	9.62E-14
Error	1,456.14	32	45.504
Total	9,478.69	34

The p-value is 0.000.

Since the p-value (0.000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we cannot conclude that all three of these groups have the same mean balance on their Visa card.