Question

The mathematics department at a certain college claims that the grades in its introductory course are distributed as follows: 11% As, 19% Bs, 35% Cs, 20% Ds and 15% Fs. In a poll of 200 randomly selected students who had completed this course it was found that 14 received As, 43 Bs, 63 Cs, 41 Ds, and 39 Fs. Does this sample contradict the department’s claim when α = 0.05? Find the test statistic χ²  to two decimals. Using the chi-square chart from your book (pg 721) find the critical value for this set of data.What is the decision about the hypothesis based on the information found?

Answer 1

Following table shows the calculations:

	p	O	E=p*200	(O-E)^2/E
	0.11	14	22	2.909090909
	0.19	43	38	0.657894737
	0.35	63	70	0.7
	0.2	41	40	0.025
	0.15	39	30	2.7
Total	1	200	200	6.991985646

Following is the test statistics:

Degree of freedom:

df = number of categories -1= 5-1=4

The critical value using table is 9.488

Since so we fail to reject the null hypothesis There is no evidence to conclude that  this sample contradicts the department’s claim when α = 0.05.