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 72 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
• 18 - Social Sciences
• 34 - Liberal Arts

Calculate theX²statistic. Select the correct answer (your answer may vary just slightly due to rounding differences, in which case just select the answer closest to yours).

a. X² = [(OF-EF)²/EF] =5.01

b. X² = [(OF-EF)²/EF] =6.33

c. X² = [(OF-EF)²/EF] =4.16

d. X² = [(OF-EF)²/EF] =4.01

Calculate the degree of freedom and then identify the critical value.

a.df = number of levels-1 = 4-1 = 3

The critical X² value for an alpha of .05 with a df of 3 is 5.992

b. df = number of levels-1 = 3-1 = 2

The critical X² value for an alpha of .05 with a df of 2 is 5.783

c. df = number of levels-1 = 3-1 = 2

The critical X² value for an alpha of .05 with a df of 2 is 5.992

d. df = number of levels-1 = 4-1 = 3

The critical X² value for an alpha of .05 with a df of 3 is 5.783

Select the correct comparison of the X²statistic with the critical value and the subsequent correct decision regarding the null hypothesis.

a. The critical value is more than theX² statistic, so the teacher can reject the null hypothesis.

b. The X² statistic is less extreme than the critical value, so the teacher fails to reject the null hypothesis.

c. The X² statistic is less extreme than the critical value, so the teacher can reject the null hypothesis.

d. The X² statistic is more extreme than the critical value, so the teacher can reject the null hypothesis.

Select the correct conclusion to the research question.

a. The types of college majors are equally popular.

b. The types of college majors are not equally popular.