The number of men and women among professors in Math, Physics, Chemistry, Lingui
ID: 3159870 • Letter: T
Question
The number of men and women among professors in Math, Physics, Chemistry, Linguistics, and English departments from a SRS of small colleges were counted, and the results are shown in the table below. Test the claim that the gender of a professor is independent of the department. Use the significance level alpha = 0.01 The test statistic is x^2 = The critical value is x^2 = Is there sufficient evidence to warrant the rejection of the claim that the gender of a professor is independent of the department? No YesExplanation / Answer
DF = (r - 1) * (c - 1) = (2 - 1) * (5 - 1)=4
Er,c = (nr * nc) / n
E1,1=55.38
E1,2=83.07
E1,3=34.81
E1,4=26.11
E1,5=50.63
E2,1=14.62
E2,2=21.93
E2,3=9.18
E2,4=6.89
E2,5=13.37
2 = [ (Or,c - Er,c)2 / Er,c ]
2 =0.385+2.336+0.041+1.936+3.151+1.150+8.848+0.152+7.337+11.930=37.27 (ANS a.)
b.0.297
c. Calculated value of the test statistic is greater than the tabulated vale.So we reject the claim that the gender of a professor is independent of department.