Question

A random group of used books was selected from a warehouse to analyze their condition. The book store believes that 22% of the books are in excellent condition, 30% are in very good condition, 19% are in fair condition, and 29% are in poor condition. Is there evidence to reject this hypothesis at significance level = .05?

Excellent: 21 Very Good: 31 Fair: 16 Poor: 11

A. There is not evidence to reject the claim that the books are distributed as claimed because the test value 7.815 < 9.259

B. There is evidence to reject the claim that the books are distributed as claimed because the test value 9.259 > 7.815

C. There is not evidence to reject the claim that the books are distributed as claimed because the test value 9.488 < 9.259

D. There is evidence to reject the claim that the books are distributed as claimed because the test value 9.259 > 9.488

Answer 1

here degree of freedom =categories-1=3

for 3 df and 0.05 level crtiical value =7.815

applying chi square goodness of fit test:

		observed	Expected		Chi square
category	Probability(p)	Oi	Ei=total*p		R2i=(Oi-Ei)2/Ei
excellent	0.220	21.000	17.380		0.754
very good	0.300	31.000	23.700		2.249
fair	0.190	16.000	15.010		0.065
poor	0.290	11.000	22.910		6.192
total	1.000	79	79		9.259

test statistic =9.259

option B is correct

There is evidence to reject the claim that the books are distributed as claimed because the test value 9.259 > 7.815