A random group of used books was selected from a warehouse to analyze their cond

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

Explanation / Answer

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:

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

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

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