SOLUTION: Grades assigned by an economics lecturer for his postgraduate coursework students at a oxford have historically followed a symmetrical distribution: 5% HDs, 25% Ds, 40% Cs, 25% Ps

Question 1177272: Grades assigned by an economics lecturer for his postgraduate coursework students at a oxford have historically followed a symmetrical distribution: 5% HDs, 25% Ds, 40% Cs, 25% Ps and 5% Fs. This year, a sample of grades revealed 11 HDs, 32 Ds, 62 Cs, 29 Ps and 16 Fs. Can you conclude, at the 1% level of significance, that this year’s marks are distributed differently from marks in the past?
Answer by CPhill(1987) (Show Source): You can put this solution on YOUR website!
We will use a chi-square goodness-of-fit test to determine if this year's grades are distributed differently from the historical distribution.
**1. Define Hypotheses:**
* **Null Hypothesis (H0):** The distribution of grades this year is the same as the historical distribution.
* **Alternative Hypothesis (H1):** The distribution of grades this year is different from the historical distribution.
**2. Set Significance Level:**
* α = 0.01
**3. Observed and Expected Frequencies:**
* Total number of students: 11 + 32 + 62 + 29 + 16 = 150
* Historical percentages: 5% HD, 25% D, 40% C, 25% P, 5% F
* Expected frequencies:
* HD: 150 * 0.05 = 7.5
* D: 150 * 0.25 = 37.5
* C: 150 * 0.40 = 60
* P: 150 * 0.25 = 37.5
* F: 150 * 0.05 = 7.5
* Observed frequencies:
* HD: 11
* D: 32
* C: 62
* P: 29
* F: 16
**4. Calculate the Chi-Square Statistic:**
* χ² = Σ [(Observed - Expected)² / Expected]
* χ² = [(11 - 7.5)² / 7.5] + [(32 - 37.5)² / 37.5] + [(62 - 60)² / 60] + [(29 - 37.5)² / 37.5] + [(16 - 7.5)² / 7.5]
* χ² = (3.5² / 7.5) + (-5.5² / 37.5) + (2² / 60) + (-8.5² / 37.5) + (8.5² / 7.5)
* χ² = (12.25 / 7.5) + (30.25 / 37.5) + (4 / 60) + (72.25 / 37.5) + (72.25 / 7.5)
* χ² = 1.6333 + 0.8067 + 0.0667 + 1.9267 + 9.6333
* χ² ≈ 14.0667
**5. Determine Degrees of Freedom:**
* Degrees of freedom (df) = number of categories - 1
* df = 5 - 1 = 4
**6. Find the Critical Chi-Square Value:**
* Using a chi-square distribution table or calculator, with df = 4 and α = 0.01, the critical chi-square value is approximately 13.277.
**7. Compare the Calculated Chi-Square and Critical Value:**
* Calculated χ² (14.0667) > Critical χ² (13.277)
**8. Make a Decision:**
* Since the calculated chi-square value is greater than the critical chi-square value, we reject the null hypothesis.
**9. Conclusion:**
* At the 1% level of significance, we can conclude that this year's marks are distributed differently from marks in the past.
Final Answer: Yes, we can conclude at the 1% level of significance that this year’s marks are distributed differently from marks in the past.

RELATED QUESTIONS
Please suggest the null and alternative hypothesis for the following problem. At... (answered by Theo)

A lecturer in a university wants to investigate the differences in students’ marks with (answered by proyaop)

A lecturer wants to know if his statistics class has a good grasp of basic maths from... (answered by robertb)

The following probabilities for grades in management science have been determined based... (answered by ewatrrr)

Textbook Question from Applied Statistics in Business and Economics, by Doane and Seward (answered by stanbon)

The professor of a introductory calculus class has stated that, historically, the... (answered by Theo)

A reading coordinator in a large public school system suspect that poor readers may test... (answered by CPhill)

6 digit passwords are randomly assigned to students by the computer department when they... (answered by jorel1380)

Question 1(a) Suppose that the amount of time teenagers spend on the Internet is... (answered by ikleyn)