Question

(i) overall proportion of left handed=57/477=0.1195

 faculty Right-handed Left-handed sum Science 101 10 111 Health science 115 26 141 Engineering 121 5 126 Arts 83 16 99 sum= 420 57 477

(ii)

 porportion of left handed porportion of left handed Expected frequency of left handed Expected frequency of left handed 10/111= 0.0901 57/4= 14.25 26/141= 0.1844 57/4= 14.25 5/126= 0.0397 57/4= 14.25 16/99= 0.1616 57/4= 14.25

(iii) null hypothesis H0: There is no association between handedness and faculty

alternate hypothesis Ha: There is association between handedness and faculty

here we use chi-square test and

chi-square=sum((O-E)2/E)=15.85 with (r-1)(c-1)=(4-1)(2-1)=2 df

p-value=0.0004

since p-value is less than typical level of significance alpha=0.05, so we fail to accept H0 and conclude that there is association between handedness and faculty.

 Observed(O) Expected(E) E (O-E) (O-E)2/E 101 111*420/477 97.74 3.26 0.11 115 141*420/477 124.15 -9.15 0.67 121 126*420/477 110.94 10.06 0.91 83 99*420/477 87.17 -4.17 0.20 10 111*57/477 13.26 -3.26 0.80 26 141*57/477 16.85 9.15 4.97 5 126*57/477 15.06 -10.06 6.72 16 99*57/477 11.83 4.17 1.47 sum= 477 0 477 1.6E-14 15.85

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