Question

An observed frequency distribution of the final grades of MAT121 is as follows:

Final Grade: A / A− / B+ / B / B− / C+ / C / C− / D / F

Frequency (O): 23 / 26 / 23 /19 / 24 / 29 / 21 / 22 / 24 / 48

At the 0.05 significance level, test the claim that the final grades of MAT121 occur with the same frequency.

The test statistic is χ2=______________

Answer 1

Solution:

Here, we have to use chi square test for goodness of fit.

Null hypothesis: H0: Each grade has same frequency.

Alternative hypothesis: Ha: Each grade doesn’t have same frequency.

We are given level of significance = α = 0.05

Test statistic formula is given as below:

Chi square = ∑[(O – E)^2/E]

Where, O is observed frequencies and E is expected frequencies.

We are given

N = 10 grades

Degrees of freedom = df = N – 1 = 10 – 1 = 9

α = 0.05

Critical value = 16.91897762

(by using Chi square table or excel)

Calculation tables for test statistic are given as below:

Grade	O	E	(O - E)^2/E
A	23	25.9	0.324710425
A-	26	25.9	0.0003861
B+	23	25.9	0.324710425
B	19	25.9	1.838223938
B-	24	25.9	0.139382239
C+	29	25.9	0.371042471
C	21	25.9	0.927027027
C-	22	25.9	0.587258687
D	24	25.9	0.139382239
F	48	25.9	18.85752896
Total	259	259	23.50965251

Test Statistic = Chi square = ∑[(O – E)^2/E] = 23.50965251

χ2 statistic = 23.50965251

P-value = 0.00514771

(By using Chi square table or excel)

P-value < α = 0.05

So, we reject the null hypothesis

There is not sufficient evidence to conclude that each grade has same frequency.