I just gave an exam to my 2 sections of MAT100 A frequency d

I just gave an exam to my 2 sections of MAT100. A frequency distribution summarizing grades of the 48 people in the population of those 2 sections is given below. Grade Frequency Use your TI to find the mean and standard deviation for class population (b) My class grade distribution MUST fit the 10% A, 20%B, 40% C, 20% D, 10% F rule that I Invented. Set up a hypothesis test to test my claimed grade distribution. Use a 5% significance level.

Solution

For finding mean and std deviation of frequency distribution, we can use midpoint for each interval.

Mean = 3760/48 = 78.33

E(X²) = 299200/48 = 6233.33

Var(x) = 97.74

Std dev=9.8864

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H0: Distribution is in the given proportion

Ha: Distribution is not in the given proportion

Two tailed chi square test

Prepare contingency table

p value = 0.3260

As p >0.05. accept null hypothesis

There is statistical evidence to prove that your claim is correct at 5% sign. level.

Midpoint x	Frequency f	f*x	f*x^2
95	7	665	63175
85	11	935	79475
75	23	1725	129375
65	5	325	21125
55	2	110	6050
Total	48	3760	299200