A random group of used books was selected from book warehouse to analyze their c

Question

A random group of used books was selected from book warehouse to analyze their condition. The book store believes that 28% of the books are in excellent condition, 38% are in very good condition, 15% are in fair condition, and 19% are in poor condition. Is there evidence to reject this hypothesis at ? :0.05? Book condition Number of books A) There is not evidence to reject the claim that the books are distributed as claimed 29. Excellent 19 Very good 31 Fair 18 Poor 10 because the test value 5.3925.392 There is evidence to reject the claim that the books are distributed as claimed because the test value 7.815>5.392 B) C) D)

Explanation / Answer

Since we are goinf to test Hypotheses for Book data store expected values becomes those which are provided by them.

Let Ho = Claim made by book store is correct

Ha = Claim made by book store is not correct

Total Books = 19 + 31 + 18 + 10 = 78

Summarized table is given below:

So, Chi square statistic = 5.491

Degree of freedom is calculated by using the following formula:
DF = (r-1)(c-1)
Where
DF = Degree of freedom
r = number of rows
c = number of columns

Degree of freedom, df = 4-1=3

So, critical value of chi square statistic for 3 degree of freedom and alpha = 0.05 is 7.815

Now 7.815 > 5.491, So we can reject the NULL HYPOTHESES.

Hence, option D) is correct

Category Number of Books-Observed(O) Percentage By book Store Values Expected by book store(E) (E-O)^2/E Excellent 19 28% 22 0.37 Very Good 31 38% 30 0.06 Fair 18 15% 12 3.39 Poor 10 19% 15 1.67 Sum 5.491

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