The director of library services at Fairmont 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.

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.
Please provide the following information.
(a) What is the level of significance? State the null and alternate hypotheses.
(b) Find the value of the chi-square statistic for the sample. Are all the expected frequencies greater than 5? What sampling distribution will you use? What are the degrees of freedom?
(c) Find or estimate the P-value of the sample test statistic.
(d) Based on your answers in parts (a)€“(c), will you reject or fail to reject the null hypothesis that the population fits the specified distribution of categories?
(e) Your conclusion in the context of the application.

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Subject Area Business Humanities Natural science Social science All other subjects Percentage of Books in Circulation Library on This Subject 3290 25% 20% 15% 896 Number of Books in Sample on This Subject 268 214 215 115 76