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 Number of Books in

Library on This Subject Sample on this subject Business 32% 269

Humanities 25% 221

Natural Science 20% 216

Social Science 15% 114

All other subjects 8% 68

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?

State the null and alternate hypotheses.

H₀: The distributions are the same.

H₁: The distributions are different.

H₀: The distributions are the same.

H₁: The distributions are the same.

H₀: The distributions are different.

H₁: The distributions are different.

H₀: The distributions are different.

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.)=