Question

To study whether or not handedness (being left or right handed) is affected by gender, 65 people were sampled. A contingency table is presented below:

Gender/Handedness
Right Left Total
Boys 21 8 29
Girls 24 12 36
Total 45 20 65

a) We wish to test the null hypothesis that the percentage of right-handed boys is the same as the percentage of right-handed girls. Test this hypothesis with a chi-square test using α = 0.05. (Don’t forget to state the null and alternative hypotheses. Don’t forget to write a conclusion.) b) Again test the

Answer 1

To test

Ho: The percentage of right handed boys is the same as the percentage of right handed girls.

H1:The percentage of right handed boys is the not same as the percentage of right handed girls.

# Observed Table:

	Right	Left	Total
Boys	21	8	29
Girls	24	12	36
total	45	20	65
# Expected Frequency (EI)=∑row*∑Column/∑Total
Expected frequency table:
	Right	Left	Total
Boys	20.07692	8.923077	29
Girls	24.92308	11.07692	36
total	45	20	65
# Chi Square (ꭓ^2)=	∑(Oi-Ei)^2/Ei
	Right	Left	Total
Boys	0.04244	0.095491	0.137931
Girls	0.034188	0.076923	0.111111
total	0.076628	0.172414	0.249042
# P value=	0.61775

Where P value > 0.05

# We accept Ho

# Conclusion: The percentage of right handed boys is the same as the percentage of right handed girls.