Answer to Question #118923 in Statistics and Probability for simran

Question

The following contingency table presents the analysis of 300 persons according to
hair colour and eye colour:
Hair Colour Eye Colour
Blue Grey Brown
Burgundy 30 10 40
Brown 40 20 40
Black 50 30 40

Test the hypothesis that there is an association between hair colour and eye colour at
5% level of significance

Answer 1

H₀ : Hair and eye colour are independent

H₁ : Hair and eye colour are associated

χ²=$\sum$^r_i=1 $\sum$ ^c_j=1=(O_ij-E_ij)²/E_ij

E_ij=R_iC_j/N, R_i - sum of i^-th row, C_j - sum of j^-th column, N - total sample size

E₁₁=(80*120)/300=32, (O₁₁-E₁₁)²=4

E₁₂=(80*60)/300=16, (O₁₂-E₁₂)²=36

E₁₃=(80*120)/300=32, (O₁₃-E₁₃)²=64

E₂₁=(100*120)/300=40, (O₂₁-E₂₁)²=0

E₂₂=(100*60)/300=20, (O₂₂-E₂₂)²=0

E₂₃=(100*120)/300=40, (O₂₃-E₂₃)²=0

E₃₁=(120*120)/300=48, (O₃₁-E₃₁)²=4

E₃₂=(120*60)/300=24, (O₃₂-E₃₂)²=36

E₃₃=(120*120)/300=48, (O₃₃-E₃₃)²=64

χ²=7.29

degrees of freedom: (r-1)(c-1)=4

the critical value of chi square with 4df at 5% level significance: 9.488

χ²<critical value, so we accept H₀ ,so hair colour is independent of eye colour