The number of men and women among professors in Math, Physics, Chemistry, Lingul

Question

The number of men and women among professors in Math, Physics, Chemistry, Lingulstics, 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 - 0.025. 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? Yes No

Explanation / Answer

a)

Doing an Expected Value Chart,          
          

          
Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    23.41720802   [ANSWER]

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b)  
          
With df = (a - 1)(b - 1), where a and b are the number of categories of each variable,          
          
a =    2      
b =    5      
          
df =    4      
          
Thus, the critical value is          
          
significance level =    0.05      
          
By table/technology,

chi^2(critical) =    9.487729037   [ANSWER]

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c)  
          
As chi^2 > 9.488, we   REJECT THE NULL HYPOTHESIS.      
Hence, there is sufficient evidence. [ANSWER: YES]

56.39628 87.15789 43.57895 31.6161 57.25077 9.603715 14.84211 7.421053 5.383901 9.749226

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