Question

In a study of the television viewing habits of children, a developmental psychologist selects a random sample of 232 first graders - 135 boys and 97 girls. Each child is asked which of the following TV programs they like best: The Lone Ranger, Sesame Street, or The Simpsons. Results are shown in the contingency table below. Using a 5% level of significance, does gender play a role in the viewing preferences?

	Viewing Preferences
	Lone Ranger	Sesame Street	The Simpsons	Row Total
Boys	72	35	28	135
Girls	20	60	17	97
Column Total	92	95	45	232

Answer 1

Ans:

Chi square test for independence:

H0:Viewing preference is independent of the gender.

Ha:Viewing preference is not independent of the gender.

	Observed(fo)
	Lone rager	Seasame street	The Simpsons	Total
Boys	72	35	28	135
Girls	20	60	17	97
Total	92	95	45	232
	Expected(fe)
	Lone rager	Seasame street	The Simpsons	Total
Boys	53.53	55.28	26.19	135
Girls	38.47	39.72	18.81	97
Total	92	95	45	232
	Chi square=(fo-fe)^2/fe
	Lone rager	Seasame street	The Simpsons	Total
Boys	6.37	7.44	0.13	13.94
Girls	8.86	10.35	0.18	19.39
Total	15.23	17.79	0.30	33.33

Test statistic:

Chi square=33.33

df=(2-1)*(3-1)=2

p-value=CHIDIST(33.33,2)=0.0000

As,p-value<0.05,we reject the null hypothesis.

There is sufficient evidence to conclude that gender play a role in the viewing preferences