Question

Grades assigned by an economics instructor have historically followed a symmetrical distribution: 5% A’s, 25% B’s, 40% C’s, 25% D’s, and 5% F’s. This year a sample of 150 grades were drawn and the grades were recorded. The sample had 11 A’s; 32 B’s; 62 C’s; 29 D’s; and 16 F’s. Can you conclude, at the 10% level of significance, that this year’s grades are distributed differently from grades in the past?

Answer 1

We are going to use chi square goodness of fit test.

To test,

H0:: 5% A’s, 25% B’s, 40% C’s, 25% D’s, and 5% F’s is the distribution of grades this year

or, p1=0.05,p2=0.25,p3=0.40,p4=0.25,p5=0.05

H1:At least one grade distribution has changed

or, at least one of the proportion have changed