Question

. Sample Ouestions #3: Here are the data from an experiment studying the effect of culture on extraversion (1-15) . Japan (n-5): 3, 5, 7,4, 3 Argentina (n-5): 9, 11, 14, 10, 10 . Kenya (n-6):9,7,8,5,8, 11 United States (n-5): 7,7,6,4,9 Can we conclude that the mean scores among the groups are different from each other?

Answer 1

The null and alternative hypothesis is

$H_{0}:\mu_{J}=\mu_{A}=\mu_{K}=\mu_{U}$

H₁ : Al least one group mean are differ to another mean group

We can use one way ANOVA to find the difference in mean.

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Japan	5	22	4.4	2.8
Argentina	5	54	10.8	3.7
Kenya	6	48	8	4
United States	5	33	6.6	3.3
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	108.0381	3	36.0127	10.34148	0.000416	3.196777
Within Groups	59.2	17	3.482353
Total	167.2381	20

The p-value is less than 0.05, we reject the null hypothesis and conclude that the mean scores among the groups are different from each others.