Question

The psychology department at a certain college claims that the grades in its introductory course are distributed as follows: 8% As, 20% Bs, 30% Cs, 22% Ds, and 20% Fs. In a poll of 200 randomly selected students who had completed this course, it was found that 16 received As; 40, Bs; 70, Cs; 43, Ds; and 31, Fs. Does this sample contradict the department's claim at the .05 level?

(a) Find the test statistic. (Give your answer correct to two decimal places.)


(ii) Find the p-value. (Give your answer bounds exactly.)
____< p < ____
(b) State the appropriate conclusion.

____Reject the null hypothesis, there is significant evidence to contradict the department's claim.

___Fail to reject the null hypothesis, there is not significant evidence to contradict the department's claim.   

____Reject the null hypothesis, there is not significant evidence to contradict the department's claim.

____Fail to reject the null hypothesis, there is significant evidence to contradict the department's claim.

Answer 1

Null Hypothesis H0: The students are distributed according to the given proportion

Alternative Hypothesis H1: The students are not distributed according to the given proportion

a)

Under H0, the calculations for expected frequencies and test statistic is

Subject	Obs. Freq. (O)	Proportion p	Exp. Freq. E = np	(O-E)^2/E
A	16	0.08	16	0.00
B	40	0.2	40	0.00
C	70	0.3	60	1.67
D	43	0.22	44	0.02
F	31	0.2	40	2.03
Total	200	1	200	3.71

The test statistic is

Degrees of freedom = n-1= 4

ii) The P-Value is .44667

0.25< p value < 0.50

iii ) Since p value is greater than significance level, Fail to REject H0.

Fail to reject the null hypothesis, there is not significant evidence to contradict the department's claim.