Q3) Chi-Square Test for Independence (8 points) This question is an extension from Q2 above. The high school teacher was also interested in whether there is a gender difference in terms of the student's choice of majors. So he broke the data down by gender in the following table and conducted a Chi-square test for independence with = .05.

Type of Major Female Male Total STEM 8 12 20 Social Sciences 10 10 20 Liberal Arts 8 2 10

a. What are the variables in this analysis? What scale of measurement is each variable (nominal, ordinal, or continuous)? (2 points)

b. State the null and alternative hypotheses in words. (1 point total)

c. Calculate X2 statistic. (2 points)

d. Calculate the degree of freedom and then identify the critical value. (1 point)

e. Compare the X2 statistic with the critical value, then report the hypothesis test result, using "reject" or "fail to reject" the null hypothesis in the answer. (1 point)

f. Explain the conclusion in a sentence or two, to answer the research question. (1 point)