You notice in your introductory psychology class that more w

You notice in your introductory psychology class that more women tend to sit up front, and more men sit in the back. To determine whether this difference is significant, you collect data on the seating preferences for the students in your class. The data follow.

Men- Front of the Room 15 Back of the Room 32

Women- Front of the Room 27 Back of the Room 19

a. What is 2obt?

b. What is df for this test?

c. What is 2cv?

d. What conclusion should be drawn from these result?

Solution

a)

Doing an Expected Value Chart,          
       Men Women          
Front       21.22580645   20.77419355  
Back       25.77419355   25.22580645
          
Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 (obt) =    6.732322624   [ANSWER]

******************  
          
b)

With df = (a - 1)(b - 1), where a and b are the number of categories of each variable,          
          
a =    2      
b =    2      
          
df =    1   [ANSWER]

**********************

c)  
          
Thus, the critical value is, using table/technology,          
          
significance level =    0.05      
          
chi^2(cv) =    3.841458821   [ANSWER]  

**********************
          
d)

As chi^2(obt) > chi^2(cV), we   REJECT THE NULL HYPOTHESIS.      
          
Thus, there is significant evidence that there is a difference between the seating preferences between genders. [CONCLUSION]