4 Please show work Is there a relationship between handednes

4. Please show work Is there a relationship between handedness and gender? A researcher collected the following data in hopes of discovering if handedness and gender are independent (Ambidextrous individuals were excluded from the study). Use the Chi-Square test for independence to explore this at a level of significance of 0.05.

Left-Handed Right-Handed

Men 13                22

Women 27            18

Solution

Doing an Expected Value Chart,          
          
17.5   17.5  
22.5   22.5  

Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    4.114285714      
          
With df = (a - 1)(b - 1), where a and b are the number of categories of each variable,          
          
a =    2      
b =    2      
          
df =    1      
          
Thus, the critical value is          
          
significance level =    0.05      
          
chi^2(critical) =    3.841458821      
          
Also, the p value is          
          
P =    0.042522478      
          
As chi^2 > 3.84146, and P < 0.05, we   REJECT THE NULL HYPOTHESIS.      
          
Thus, there is significant evidence that handedness is not independent to gender at 0.05 level. [CONCLUSION]