In: Statistics and Probability
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
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.