In the past, the numbers of A\'s, B\'s, C\'s, D\'s and F\'s given in a statistic

Question

In the past, the numbers of A's, B's, C's, D's and F's given in a statistics class has been 8%, 17%, 45%, 22%, and 8%, respectively. A new teaching method was adopted last semester and there were 10 A's, 20 B's, 10 C's, 5 D's, 5 F's. At an alpha level of .05, test the hypothesis that the new method produces the same proportion of each grade type as before.

(a) What are the expected number of each grade type?

(b) What is the computed X^2 value?

(c) What is the df?

(d) What is the tabled X^2 value?

(e) What is your decision about Ho? (Accept or reject)

(f) What does this mean in terms of the scenario above?

Explanation / Answer

a)

There are 50 participants, so the expected values are

A   4
B   8.5
C   22.5
D   11
F   4

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b)

Doing an observed/expected value table,          
O   E   (O - E)^2/E  
10   4   9  
20   8.5   15.55882353  
10   22.5   6.944444444  
5   11   3.272727273  
5   4   0.25  
          
Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    35.02599525   [ANSWER]

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c)  
          
As df = a - 1,           
          
a = number of groups =   5      
df = a - 1 =    4   [ANSWER]  
          
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d)

Then, the critical chi^2 value is          
          
significance level =    0.05      

chi^2(crit) =    9.4877   [ANSWER]  

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e)

As chi^2 > 9.4877, then we REJECT HO.

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f)

Hence, there is significant evidence that the distribution of grades is not 8%, 17%, 45%, 22%, and 8%, respectively for A's, B's, C's, D's and F's at 0.05 level. [CONCLUSION]

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