1. Historically, the grade distribution on a final exam for a mathclass has been as follows:Historically, Across DepartmentAsBsCsDsFs15%20%40%15%10%After implementing a new teaching method, the final exam gradedistribution (in counts) for 300 students was as follows:AsBsCsDsFs60501304020

Question
Asked Nov 22, 2019
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Does the new method appear to lead to a new grade distribution? Test at the 5% significance level. Also, is the new method better? Explain.

1. Historically, the grade distribution on a final exam for a math
class has been as follows:
Historically, Across Department
As
Bs
Cs
Ds
Fs
15%
20%
40%
15%
10%
After implementing a new teaching method, the final exam grade
distribution (in counts) for 300 students was as follows:
As
Bs
Cs
Ds
Fs
60
50
130
40
20
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1. Historically, the grade distribution on a final exam for a math class has been as follows: Historically, Across Department As Bs Cs Ds Fs 15% 20% 40% 15% 10% After implementing a new teaching method, the final exam grade distribution (in counts) for 300 students was as follows: As Bs Cs Ds Fs 60 50 130 40 20

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Expert Answer

Step 1

Given data

As
Bs
Cs
Ds
Fs
Total
15%
15%
10%
20%
40%
100
Observed
60
50
20
300
130
40
300 х 0.10
300 x 0.15
Expected
300 х 0.20
300 х 0.40
300 х 0.15
300
-60
45
- 120
- 45
- 30
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As Bs Cs Ds Fs Total 15% 15% 10% 20% 40% 100 Observed 60 50 20 300 130 40 300 х 0.10 300 x 0.15 Expected 300 х 0.20 300 х 0.40 300 х 0.15 300 -60 45 - 120 - 45 - 30

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Step 2

Formulation of Hypothesis
Null Hypothesis H0: - The distribution of the grade is same as mentioned percentage distribution.
Alternative Hypothesis H1: - The distributi...

E;
(60 60)2 (50 - 45)2 (130 120)2 (40 45)2 (20 30)2
_
x2
= 5.28
120
45
60
45
30
Degree of freedom is given by
d. o.f (no of rows 1) x (no of columns - 1)
(2 - 1) x (5 - 1)
1 x 4 4
Finding the critical chi-square value
CHISQ.INV.RT (0.05,4))
x0.05,4
= 9.48 (FROM EXCEL
11
x2 x0.01.2
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E; (60 60)2 (50 - 45)2 (130 120)2 (40 45)2 (20 30)2 _ x2 = 5.28 120 45 60 45 30 Degree of freedom is given by d. o.f (no of rows 1) x (no of columns - 1) (2 - 1) x (5 - 1) 1 x 4 4 Finding the critical chi-square value CHISQ.INV.RT (0.05,4)) x0.05,4 = 9.48 (FROM EXCEL 11 x2 x0.01.2

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