2. The chair of the business department hypothesizes that the final grades in a

Question

2. The chair of the business department hypothesizes that the final grades in a statistics course are distributed as 30% As, 40% Bs, 20% Cs, and 10% D or Fs. At the end of the semester, the following numbers of grades were earned. Grade A B C D, F Number 14 21 11 4 Does the grade distribution match the department hypothesis? To test this, 1). Find the expected numbers for getting these grades. 2). Calculate the chi-square value for this table. 3). Determine whether P-value is larger than or less than 0.05? 4). Make your conclusion at significance level 0.05.

Explanation / Answer

Ans:

1)Expected counts are 50*0.3=15,50*0.4=20.50*0.2=10,50*0.1=5

2)Chi square value=0.417

(see the table above)

3)df=4-1=3

p-value=CHIDIST(0.417,3)=0.9368

p-value>0.05

4)As,p-value>0.05,we do not reject null hypothesis.

We can conclude that Grade distribution match the department hypothesis.

Observed(O) Expected(E) (O-E)^2/E A 14 15 0.067 B 21 20 0.05 C 11 10 0.1 D,F 4 5 0.2 Total 50 50 0.417

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