Question

A biology professor claims that, on the average, 10% of her students get a grade of A, 30% get a B, 40% get a C, 10% get a D, and 10% get an F. The grades of a random sample of 100 students were recorded. The following table presents the results. Grade A B C D F Observed 10 34 46 6 4 Test the hypothesis that the grades follow the distribution claimed by the professor. Use the α = 0.05 level of significance.

Answer 1

H0: The grades follow the distribution claimed by the professor

Ha: The grades do not follow the distribution claimed by the professor

A survey of 100 students were recorded.

Professor predicted 10 % of students grade is A, 30 % of students grade is B, 40 % of students grade is C, 10 % of students grade is D, 10 % of students grade is F

I find expected students who will get A = 100 *10 /100 =10

similarly I find for all the other grades as summarized below-

Grade	Observed frequency	Expected Frequency
A	10	10
B	34	30
C	46	40
D	6	10
F	4	10

I shall test for 2 ( Chi Square ) goodness of fit.

2 = ( Observed - Expected )2 / Expected

= (10 -10)^2 / 10 + ( 34 - 30)^2 / 30 + ( 46 -40)^2 / 40+ ( 6-10)^2 / 10 + ( 4-10)^2 / 10= 6.633

Since there are 5 groups so degrees of freedom is 4 .

2 =0.05,4  = 9.488 > 6.633

so, we fail to reject null hypothesis.

There is not enough evidence to reject that the grades follow the distribution claimed by the professor.

So, The grades follow the distribution claimed by the professor.

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