Professor Fair believes that extra time does not improve grades on exams. He randomly divided a group of 300 students into two groups and gave them all the same test. One group had exactly 1 hour in which to finish the test, and the other group could stay as long as desired. The results are shown in the following table. Test at the 0.01 level of significance that time to complete a test and test results are independent. Time 1h A 22 Unlimited 17 49 84 Column Total 39 92 148 B 43 C 64 F 12 9 21 Chi-square test of independence Chi-square for testing oor o (1) Give the value of the level of significance. Row Total 141 159 300 Classify the problem as one of the following: Chi-square test of independence or homogeneity, Chi-square goodness of fit, Chi-square for testing o ² or o. Chi-square test of homogeneity Chi-square goodness of fit State the null and alternate hypotheses. Ho: The distributions for a timed test and an unlimited test are different. H: The distributions for a timed test and an unlimited test are the same. Ho: Time to take a test and test score are not independent. H: Time to take a test and test score are independent. Ho: The distributions for a timed test and an unlimited test are the same. H: The distributions for a timed test and an unlimited test are different. He: Time to take a test and test score are independent. H: Time to take a test and test score are not independent.
Professor Fair believes that extra time does not improve grades on exams. He randomly divided a group of 300 students into two groups and gave them all the same test. One group had exactly 1 hour in which to finish the test, and the other group could stay as long as desired. The results are shown in the following table. Test at the 0.01 level of significance that time to complete a test and test results are independent. Time 1h A 22 Unlimited 17 49 84 Column Total 39 92 148 B 43 C 64 F 12 9 21 Chi-square test of independence Chi-square for testing oor o (1) Give the value of the level of significance. Row Total 141 159 300 Classify the problem as one of the following: Chi-square test of independence or homogeneity, Chi-square goodness of fit, Chi-square for testing o ² or o. Chi-square test of homogeneity Chi-square goodness of fit State the null and alternate hypotheses. Ho: The distributions for a timed test and an unlimited test are different. H: The distributions for a timed test and an unlimited test are the same. Ho: Time to take a test and test score are not independent. H: Time to take a test and test score are independent. Ho: The distributions for a timed test and an unlimited test are the same. H: The distributions for a timed test and an unlimited test are different. He: Time to take a test and test score are independent. H: Time to take a test and test score are not independent.
Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter11: Data Analysis And Displays
Section: Chapter Questions
Problem 1CA
Related questions
Question
Transcribed Image Text:Professor Fair believes that extra time does not improve grades on exams. He randomly divided a group
of 300 students into two groups and gave them all the same test. One group had exactly 1 hour in which
to finish the test, and the other group could stay as long as desired. The results are shown in the
following table. Test at the 0.01 level of significance that time to complete a test and test results are
independent.
Time
1h
A
22
Unlimited
17
Column Total 39
B
43
49
92
C
64
84
148
F
12
9
21
Row Total
141
159
300
Classify the problem as one of the following: Chi-square test of independence or homogeneity, Chi-square
goodness of fit, Chi-square for testing oor o
Chi-square goodness of fit
Chi-square test of independence Chi-square test of homogeneity
Chi-square for testing oor o
(i) Give the value of the level of significance.
State the null and alternate hypotheses.
Ho: The distributions for a timed test and an unlimited test are different.
H₁: The distributions for a timed test and an unlimited test are the same. Ho: Time to take a test and
test score are not independent.
H: Time to take a test and test score are independent.
unlimited test are the same.
Ho: The distributions for a timed test and an
H: The distributions for a timed test and an unlimited test are different. Ho: Time to take a test and
test score are independent.
H₁: Time to take a test and test score are not independent.
(ii) Find the sample test statistic. (Round your answer to two decimal places.)
(iii) Find or 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 < 0.0250
(iv) Conclude the test.
Since the P-value < x, we fail to reject the null hypothesis. Since the P-valueza, we reject the null
hypothesis. Since the P-value is zx, we fail to reject the null hypothesis. Since the P-value < x,
we reject the null hypothesis.
(v) Interpret the conclusion the context of the application.
At the 1% level of significance, there insufficient evidence to claim that time to do a test and test
results are not independent. At the 1% level of significance, there is sufficient evidence to claim that
time to do a test and test results are not independent.
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