Question

An observed frequency distribution of the final grades of a class is as follows: Final Grade...

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

Final Grade AA A−A− B+B+ BB B−B− C+C+ CC C−C− DD FF
Frequency (O) 50 53 47 50 54 50 46 44 54 52

At the 0.025 significance level, we wish to test the claim that the final grades of such a class occur with the same frequency.
1. The expected frequency is E=E=

2. Fill in the following table

Final Grade Frequency (O) (O−E)2E(O−E)2E
AA 50
A−A− 53
B+B+ 47
BB 50
B−B− 54
C+C+ 50
CC 46
C−C− 44
DD 54
FF 52


3. The test statistic is χ2=χ2=
4. The critical value is
5. The conclusion is
A. There is not sufficient evidence to warrant the rejection of the claim that the final grades of such a class occur with the same frequency.
B. There is sufficient evidence to warrant the rejection of the claim that the final grades of such a class occur with the same frequency.

Homework Answers

Answer #1
Final Grade Frequency (O) Expected proportion. Expected Frequency ( E) ( O-E)^2 ( O-E)^2/E
AA 50 0.1 50 0 0
A−A− 53 0.1 50 9 0.18
B+B+ 47 0.1 50 9 0.18
BB 50 0.1 50 0 0
B−B− 54 0.1 50 16 0.32
C+C+ 50 0.1 50 0 0
CC 46 0.1 50 16 0.32
C−C− 44 0.1 50 36 0.72
DD 54 0.1 50 16 0.32
FF 52 0.1 50 4 0.08
Total 500 1 500 106 2.12

3. The test statistic is χ2= 2.12

4. The critical value is

df = 10 - 1 = 9

alpha = 0.025

χ2_c = 19.02

As

χ2 = 2.12 < χ2_c = 19.02 we failed to reject the null hypothesis

5. The conclusion is

A. There is not sufficient evidence to warrant the rejection of the claim that the final grades of such a class occur with the same frequency

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