Q2) Chi-Square Test for Goodness of Fit (7 points) A high school physics teacher wondered if his students in the senior class this year will be more likely to go into STEM (Science, Technology, Engineering, Mathematics) majors than Social Science and Liberal Arts majors. He asked each of his 50 students about their first choice for major on their college applications and conducted a Chi-square test for goodness of fit with an alpha level of .05 to see if the number of students choosing each category differs significantly. 20 - STEM 20 - Social Sciences 10 - Liberal Arts

a. What is the variable in this test? What type of variable is it (nominal, ordinal, or continuous)? (1 point)

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

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)