Question

test the hypothesis that gender and eye color are independent at 5%level of significance. State clearly the null hypothesis, alternative hypothesis, illustrate the rejection region, and critical value. and interpret your results.

..........male female total

brown 5 20 . 25

blue . 25    25 50

other 30 45 75

total . 60 90 150

Answer 1

	Male	Female	Total
Brown	5	20	25
Blue	25	25	50
Other	30	45	75
Total	60	90	150

The null and alternative hypothesis is

H0: Gender and eye color are independent.

H1: Gender and eye color are not independent.

Level of significance = 0.05

Test statistic is

O: Observed frequency
E: Expected frequency.
E = ( Row total*Column total) / Grand total

O	E	(O-E)	(O-E)^2	(O-E)^2/E
5	10	-5	25	2.5000
20	15	5	25	1.6667
25	20	5	25	1.2500
25	30	-5	25	0.8333
30	30	0	0	0.0000
45	45	0	0	0.0000
			Total	6.25

Degrees of freedom = ( Number of rows - 1 ) * ( Number of column - 1) = ( 3 - 1) * (2 - 1) = 2 * 1 = 2

Critical value = 5.991

( From chi-square table)

Test statistic > critical value we reject null hypothesis.

Conclusion:

Gender and eye color are not independent.