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. Percent of Books on Subject in Circulation Library on This Subject Number of Books in Subject Area Sample on This Subject Business Humanities Natural Science Social Science All other subjects 32% 279 25% 20% 201 214 15% 124 8% 70 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. O Ho: The distributions are different. H,: The distributions are the same. O Ho: The distributions are the same. H: The distributions are the same. O Hg: The distributions are the same. H: The distributions are different. O Ho: The distributions are different. H4: The distributions are different. (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? O Yes O No What sampling distribution will you use? O chi-square O student's t O binomial O uniform O normal What are the degrees of freedom?

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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.

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.
Percent of Books on Subject in Circulation
Library on This Subject
Number of Books in
Subject Area
Sample on This Subject
32%
25%
20%
Business
279
Humanities
201
Natural Science
214
Social Science
15%
124
All other subjects
8%
70
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.
O Ho: The distributions are different.
H,: The distributions are the same.
O Hn: The distributions are the same.
H,: The distributions are the same.
O Hn: The distributions are the same.
H,: The distributions are different.
O Ho: The distributions are different.
H,: The distributions are different.
(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?
O Yes
O No
What sampling distribution will you use?
O chi-square
O student's t
O binomial
O uniform
O normal
What are the degrees of freedom?
Transcribed Image Text: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. Percent of Books on Subject in Circulation Library on This Subject Number of Books in Subject Area Sample on This Subject 32% 25% 20% Business 279 Humanities 201 Natural Science 214 Social Science 15% 124 All other subjects 8% 70 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. O Ho: The distributions are different. H,: The distributions are the same. O Hn: The distributions are the same. H,: The distributions are the same. O Hn: The distributions are the same. H,: The distributions are different. O Ho: The distributions are different. H,: The distributions are different. (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? O Yes O No What sampling distribution will you use? O chi-square O student's t O binomial O uniform O normal What are the degrees of freedom?
(c) Estimate the P-value of the sample test statistic.
O P-value > 0.100
O 0.050 < P-value < 0.100
O 0.025 < P-value <0.050
O 0.010 < P-value < 0.025
O 0.005 < P-value < 0.010
O p-value < 0.005
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence?
O Since the p-value > a, we fail to reject the null hypothesis.
O Since the P-value > a, we reject the null hypothesis.
O Since the P-value sa, we reject the null hypothesis.
O since the P-value sa, we fail to reject the null hypothesis.
(e) Interpret your conclusion in the context of the application.
O At the 5% level of significance, the evidence is sufficient to conclude that the subject distribution of books in the library is different from that of books checked out by students.
O At the 5% level of significance, the evidence is insufficient to conclude that the subject distribution of books in the library is different from that of books checked out by students.
Transcribed Image Text:(c) Estimate the P-value of the sample test statistic. O P-value > 0.100 O 0.050 < P-value < 0.100 O 0.025 < P-value <0.050 O 0.010 < P-value < 0.025 O 0.005 < P-value < 0.010 O p-value < 0.005 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence? O Since the p-value > a, we fail to reject the null hypothesis. O Since the P-value > a, we reject the null hypothesis. O Since the P-value sa, we reject the null hypothesis. O since the P-value sa, we fail to reject the null hypothesis. (e) Interpret your conclusion in the context of the application. O At the 5% level of significance, the evidence is sufficient to conclude that the subject distribution of books in the library is different from that of books checked out by students. O At the 5% level of significance, the evidence is insufficient to conclude that the subject distribution of books in the library is different from that of books checked out by students.
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