The target grade distribution for a particular course is 10% A, 30% B, 40% C, 15% D, 5% F.Students complain that a particular professor who teaches this course is much harder than others.They survey 152 former students of this professor's class and find they received the following grades: 10 A, 44 B, 64 C, 23 D, 11 F.Conduct a χ2 goodness-of-fit test to see if the data provide sufficient evidence to support the students' complaint.Select the appropriate critical value (CV), test statistic (TS), and decision.(Use α = 0.10.)
A) CV = 13.2767, TS = 519.80, reject H₀
B) CV = 9.2364, TS = 3.5263, fail to reject H₀
C) CV = 7.7794, TS = 519.80, reject H₀
D) CV = 7.7794, TS = 3.5263, fail to reject H₀

Question

Quizplus · Accepted Answer

To conduct a chi-square goodness-of-fit test, we need to calculate the expected frequencies for each grade based on the target grade distribution.

Expected frequencies:
- A: 152*0.10 = 15.2
- B: 152*0.30 = 45.6
- C: 152*0.40 = 60.8
- D: 152*0.15 = 22.8
- F: 152*0.05 = 7.6

Next, we calculate the chi-square test statistic using the formula:

χ2 = Σ ( (O - E)2 / E )

where O = observed frequency and E = expected frequency.

Plugging in the values:

χ2 = [(10 - 15.2)2/15.2] + [(44 - 45.6)2/45.6] + [(64 - 60.8)2/60.8] + [(23 - 22.8)2/22.8] + [(11 - 7.6)2/7.6]

χ2 = 3.5263

The degrees of freedom for this test is df = number of categories - 1 = 5 - 1 = 4.

Using a chi-square distribution table at α = 0.10 level of significance, the critical value is 7.7794. Since our calculated chi-square statistic (3.5263) is less than the critical value, we fail to reject the null hypothesis.

Therefore, the data do not provide sufficient evidence to support the students' complaint that this particular professor is much harder than others.

The Target Grade Distribution for a Particular Course Is 10