A group of 500 individuals were asked to cast their votes re

A group of 500 individuals were asked to cast their votes regarding a particular issue of the equal rights amendment. we are interested in determining if the votes cast is independent of the sex of the individuals. the following contingency table shoes the results of the votes:

sex favor undecided oppose total

female 180 80 40 300

male 150 20 30 200

total 330 100 70 500

a. state the null and alternative hypothesis

b. show the contingency table of the expected frequencies

c. compute the test statistic

d. the null hypothesis is to be tested at 95% confidence. Determine the critical value for this test. what do you conclude?

SHOW WORK PLEASE!   

Solution

a)

Ho: THe votes cast are independent of sex.

Ha: The votes cast are not dependent of sex.

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b)

c)

Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    20.995671 [ANSWER]

d)

With df = (a - 1)(b - 1), where a and b are the number of categories of each variable,          
          
a =    3      
b =    2      
          
df =    2      
          
Thus, the critical value is          
          
significance level =    0.05      
          
chi^2(critical) =    5.991464547 [ANSWER]

So, as chi^2 > chi^2(Critical), WE REJECT THE NULL HYPOTHESIS.

Thus, there is significant evidence that the votes cast is not independent of the sex of the individuals. [CONCLUSION]