A high school physics teacher wondered if his students in thesenior class this year will be more likely to go into STEM(Science, Technology, Engineering, Mathematics) majors than SocialScience and Liberal Arts majors. He asked each of his 65 studentsabout their first choice for major on their college applicationsand conducted a Chi-square test for goodness of fit with an alphalevel of .05 to see if the number of students choosing eachcategory differs significantly.

35 – STEM

20 – Social Sciences

10 – Liberal Arts

a. What is the variable in this test? What type of variable isit (nominal, ordinal, or continuous)? (1 point total: .5 for eachquestion)

b. State the null and alternative hypotheses in words (1 pointtotal: .5 for each hypothesis)

c. Calculate X² statistic (2 pointstotal: 1 for final answer, 1 for the process of calculating it)

d. Calculate the degree of freedom and then identify thecritical value (1 point total: .5 for df, .5 for criticalvalue)

e. Compare the X² statistic withthe critical value, then report the hypothesis test result, using“reject” or “fail to reject” the null hypothesis in the answer (1point total, .5 for each answer)

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