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 Business Humanities Natural Science Social Science All other subjects USE SALT Percent of Books on Subject in Circulation Library on This Subject 32% 25% 20% 15% 8% State the null and alternate hypotheses. Ho: The distributions are different. H: The distributions are different. H: The distributions are different. H: The distributions are the same. H: The distributions are the same. distribution of books checked out by students. (a) What is the level of significance? Number of Books in Sample on This Using a 5% level of significance, test the claim that the subject distribution of books in the library fits the O Ho: The distributions are the same. Ho: The distributions are the same. Ho: The distributions are different. Are all the expected frequencies greater than 5? Yes No Subject 267 What sampling distribution will you use? chi-square binomial normal uniform Student's t What are the degrees of freedom? 218 216 106 81 (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.) (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 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence? Since the P-value > a, we fail to reject the null hypothesis. Since the P-value> x, we reject the null hypothesis. Since the P-values a, we reject the null hypothesis. Since the P-values a, we fail to reject the null hypothesis. (e) Interpret your conclusion in the context of the application. 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. 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.
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 Business Humanities Natural Science Social Science All other subjects USE SALT Percent of Books on Subject in Circulation Library on This Subject 32% 25% 20% 15% 8% State the null and alternate hypotheses. Ho: The distributions are different. H: The distributions are different. H: The distributions are different. H: The distributions are the same. H: The distributions are the same. distribution of books checked out by students. (a) What is the level of significance? Number of Books in Sample on This Using a 5% level of significance, test the claim that the subject distribution of books in the library fits the O Ho: The distributions are the same. Ho: The distributions are the same. Ho: The distributions are different. Are all the expected frequencies greater than 5? Yes No Subject 267 What sampling distribution will you use? chi-square binomial normal uniform Student's t What are the degrees of freedom? 218 216 106 81 (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.) (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 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence? Since the P-value > a, we fail to reject the null hypothesis. Since the P-value> x, we reject the null hypothesis. Since the P-values a, we reject the null hypothesis. Since the P-values a, we fail to reject the null hypothesis. (e) Interpret your conclusion in the context of the application. 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. 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.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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.
Subject Area
Business
Humanities.
Natural Science
Social Science
All other subjects
USE SALT
Percent of Books on Subject in Circulation
Library on This Subject
32%
25%
20%
15%
8%
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.
Ho: The distributions are different.
H₁: The distributions are different.
H: The distributions are different.
H: The distributions are the same.
H₁: The distributions are the same.
Ho: The distributions are the same.
Ho: The distributions are the same.
Ho: The distributions are different.
Number of Books in
Sample on This
Subject
267
218
216
106
81
(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?
chi-square binomial normal uniform m Student's t
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
0.005 < P-value < 0.010 P-value < 0.005
0.025 < P-value < 0.050 0.010< P-value < 0.025
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of
independence?
Since the P-value > a, we fail to reject the null hypothesis. Since the P-value > a, we reject the null
hypothesis. Since the P-value ≤ xx, we reject the null hypothesis. Since the P-values x, we fail
to reject the null hypothesis.
(e) Interpret your conclusion in the context of the application.
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. 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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