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A USE SALT (a) a = 0.05, df = 4, x² = 10.25 O We would reject Ho. O We would fail to reject Hg. (b) a = 0.01, df = 3, x² = 8.55 O We would reject Ho- O We would fail to reject Hg- (c) a = 0.10, df = 2, x² = 4.46 O We would reject Ho. O We would fail to reject Hg. (d) a = 0.01, k = 6, x² = 11.40 O We would reject Ho. O We would fail to reject Ho-

A USE SALT (a) a = 0.05, df = 4, x² = 10.25 O We would reject Ho. O We would fail to reject Hg. (b) a = 0.01, df = 3, x² = 8.55 O We would reject Ho- O We would fail to reject Hg- (c) a = 0.10, df = 2, x² = 4.46 O We would reject Ho. O We would fail to reject Hg. (d) a = 0.01, k = 6, x² = 11.40 O We would reject Ho. O We would fail to reject Ho-

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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**Chi-Squared Test Decision Guidelines** For an upper-tailed chi-squared test, the decision on whether to reject the null hypothesis (\(H_0\)) is based on comparing the calculated chi-squared value (\(\chi^2\)) to a critical value determined by the significance level (\(\alpha\)) and the degrees of freedom (\(df\)). Below are scenarios given with applicable decisions: (a) **Scenario:** - Significance level (\(\alpha\)) = 0.05 - Degrees of freedom (\(df\)) = 4 - Calculated chi-squared value (\(\chi^2\)) = 10.25 **Conclusion Options:** - We would reject \(H_0\). - We would fail to reject \(H_0\). (b) **Scenario:** - Significance level (\(\alpha\)) = 0.01 - Degrees of freedom (\(df\)) = 3 - Calculated chi-squared value (\(\chi^2\)) = 8.55 **Conclusion Options:** - We would reject \(H_0\). - We would fail to reject \(H_0\). (c) **Scenario:** - Significance level (\(\alpha\)) = 0.10 - Degrees of freedom (\(df\)) = 2 - Calculated chi-squared value (\(\chi^2\)) = 4.46 **Conclusion Options:** - We would reject \(H_0\). - We would fail to reject \(H_0\). (d) **Scenario:** - Significance level (\(\alpha\)) = 0.01 - Degrees of freedom (\(df\)) = 6 - Calculated chi-squared value (\(\chi^2\)) = 11.40 **Conclusion Options:** - We would reject \(H_0\). - We would fail to reject \(H_0\). To determine the correct decision for each scenario, compare the calculated chi-squared value with the critical value from the chi-squared distribution table for the given \(\alpha\) and \(df\). If the calculated value exceeds the critical value, reject \(H_0\).
Transcribed Image Text:**Chi-Squared Test Decision Guidelines** For an upper-tailed chi-squared test, the decision on whether to reject the null hypothesis (\(H_0\)) is based on comparing the calculated chi-squared value (\(\chi^2\)) to a critical value determined by the significance level (\(\alpha\)) and the degrees of freedom (\(df\)). Below are scenarios given with applicable decisions: (a) **Scenario:** - Significance level (\(\alpha\)) = 0.05 - Degrees of freedom (\(df\)) = 4 - Calculated chi-squared value (\(\chi^2\)) = 10.25 **Conclusion Options:** - We would reject \(H_0\). - We would fail to reject \(H_0\). (b) **Scenario:** - Significance level (\(\alpha\)) = 0.01 - Degrees of freedom (\(df\)) = 3 - Calculated chi-squared value (\(\chi^2\)) = 8.55 **Conclusion Options:** - We would reject \(H_0\). - We would fail to reject \(H_0\). (c) **Scenario:** - Significance level (\(\alpha\)) = 0.10 - Degrees of freedom (\(df\)) = 2 - Calculated chi-squared value (\(\chi^2\)) = 4.46 **Conclusion Options:** - We would reject \(H_0\). - We would fail to reject \(H_0\). (d) **Scenario:** - Significance level (\(\alpha\)) = 0.01 - Degrees of freedom (\(df\)) = 6 - Calculated chi-squared value (\(\chi^2\)) = 11.40 **Conclusion Options:** - We would reject \(H_0\). - We would fail to reject \(H_0\). To determine the correct decision for each scenario, compare the calculated chi-squared value with the critical value from the chi-squared distribution table for the given \(\alpha\) and \(df\). If the calculated value exceeds the critical value, reject \(H_0\).
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