Question

The director of library services at a college did a survey of types of books (by subject) in the circulation library. Then she used library records to take a random sample of 888 books checked out last term and classified the books in the sample by subject. The results are shown below.

Subject Area Percent of Books on Subject in Circulation Library on This Subject Number of Books in Sample on This Subject Business 32% 263 Humanities 25% 225 Natural Science 20% 205 Social Science 15% 110 All other subjects 8% 85 Using a 5% level of significance, test the claim that the subject distribution of books in the library fits the distribution of books checked out by students.

(a) What is the level of significance? 0.05 State the null and alternate hypotheses. H0: The distributions are different. H1: The distributions are different. H0: The distributions are different. H1: The distributions are the same. H0: The distributions are the same. H1: The distributions are different. H0: The distributions are the same. H1: The distributions are the same.

(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to three decimal places. Round the test statistic to three decimal places.) Are all the expected frequencies greater than 5?
***Yes No

***What sampling distribution will you use? uniform Student's t chi-square binomial normal What are the degrees of freedom?

(c) Estimate the P-value of the sample test statistic. P-value > 0.100 0.050 < P-value < 0.100 0.025 < P-value < 0.050 0.010 < P-value < 0.025 0.005 < P-value < 0.010 P-value < 0.005

Answer 1

a) level of significance? 0.05

H0: The distributions are the same. H1: The distributions are different.

b)

applying chi square test:

	relative	observed	Expected	residual	Chi square
category	frequency	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
1	0.320	263	284.16	-1.26	1.576
2	0.250	225	222.00	0.20	0.041
3	0.200	205	177.60	2.06	4.227
4	0.150	110	133.20	-2.01	4.041
5	0.080	85	71.04	1.66	2.743
total	1.000	888	888		12.628

value of the chi-square statistic =X² =12.628

Are all the expected frequencies greater than 5? YEs

degrees of freedom =categories-1=4

0.010 < P-value < 0.025