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The table to the right contains observed values and expected values in parentheses for two categorical variables, X and Y, where variable X has three categories and variable Y has two categories. Use the table to complete parts (a) and (b) below. Click the icon to view the Chi-Square table of critical values. (a) Compute the value of the chi-square test statistic. x = (Round to three decimal places as needed.) (b) Test the hypothesis that X and Y are independent at the a= 0.05 level of significance. OA. Ho: The Y category and X category have equal proportions. H₁: The proportions are not equal. OB. Ho: The Y category and X category are independent. H₁: The Y category and X category are dependent. OC. H: The Y category and X category are dependent. H₁: The Y category and X category are independent. OD. Ho: Ex and μ = Ey H₁: #Ex or μy #Ey What range of P-values does the test statistic correspond to? The P-value is Should the null hypothesis be rejected? O A. Yes, reject Ho. There is not sufficient evidence at the a= 0.05 level of significance to conclude that X and Y are dependent because the P-value>< O B. No, do not reject Ho. There is sufficient evidence at the a= 0.05 level of significance to conclude that X and Y are dependent because the P-value a O D. Yes, reject Ho. There is not sufficient evidence at the a= 0.05 level of significance to conclude that X and Y are dependent because the P-value

The table to the right contains observed values and expected values in parentheses for two categorical variables, X and Y, where variable X has three categories and variable Y has two categories. Use the table to complete parts (a) and (b) below. Click the icon to view the Chi-Square table of critical values. (a) Compute the value of the chi-square test statistic. x = (Round to three decimal places as needed.) (b) Test the hypothesis that X and Y are independent at the a= 0.05 level of significance. OA. Ho: The Y category and X category have equal proportions. H₁: The proportions are not equal. OB. Ho: The Y category and X category are independent. H₁: The Y category and X category are dependent. OC. H: The Y category and X category are dependent. H₁: The Y category and X category are independent. OD. Ho: Ex and μ = Ey H₁: #Ex or μy #Ey What range of P-values does the test statistic correspond to? The P-value is Should the null hypothesis be rejected? O A. Yes, reject Ho. There is not sufficient evidence at the a= 0.05 level of significance to conclude that X and Y are dependent because the P-value>< O B. No, do not reject Ho. There is sufficient evidence at the a= 0.05 level of significance to conclude that X and Y are dependent because the P-value a O D. Yes, reject Ho. There is not sufficient evidence at the a= 0.05 level of significance to conclude that X and Y are dependent because the P-value

MATLAB: An Introduction with Applications
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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The table to the right contains observed values and expected values in parentheses for two categorical variables, X and Y, where variable X has three categories and variable Y has two categories. Use the table to complete parts (a) and (b) below. Click the icon to view the Chi-Square table of critical values. (a) Compute the value of the chi-square test statistic. x=(Round to three decimal places as needed.) (b) Test the hypothesis that X and Y are independent at the a= 0.05 level of significance. O A. Ho: The Y category and X category have equal proportions. H₁: The proportions are not equal. O B. Ho: The Y category and X category are independent. H₁: The Y category and X category are dependent. OC. Ho: The Y category and X category are dependent. H₁: The Y category and X category are independent. O D. Ho: Ex and μy = Ey H₁: #Ex or μy # Ey What range of P-values does the test statistic correspond to? The P-value is Should the null hypothesis be rejected? O A. Yes, reject Ho. There is not sufficient evidence at the a= 0.05 level of significance to conclude that X and Y are dependent because the P-value > α. O B. No, do not reject Ho. There is sufficient evidence at the a= 0.05 level of significance to conclude that X and Y are dependent because the P-value <α. O C. No, do not reject Ho. There is not sufficient evidence at the a= 0.05 level of significance to conclude that X and Y are dependent because the P-value > α. O D. Yes, reject Ho. There is not sufficient evidence at the a= 0.05 level of significance to conclude that X and Y are dependent because the P-value < α. M₁₂₁ Y₂ X₁ 31 45 53 (33.50) (46.33) (49.18) X₂ X3 P 16 20 16 (13.50) (18.67) (19.82)
Transcribed Image Text:The table to the right contains observed values and expected values in parentheses for two categorical variables, X and Y, where variable X has three categories and variable Y has two categories. Use the table to complete parts (a) and (b) below. Click the icon to view the Chi-Square table of critical values. (a) Compute the value of the chi-square test statistic. x=(Round to three decimal places as needed.) (b) Test the hypothesis that X and Y are independent at the a= 0.05 level of significance. O A. Ho: The Y category and X category have equal proportions. H₁: The proportions are not equal. O B. Ho: The Y category and X category are independent. H₁: The Y category and X category are dependent. OC. Ho: The Y category and X category are dependent. H₁: The Y category and X category are independent. O D. Ho: Ex and μy = Ey H₁: #Ex or μy # Ey What range of P-values does the test statistic correspond to? The P-value is Should the null hypothesis be rejected? O A. Yes, reject Ho. There is not sufficient evidence at the a= 0.05 level of significance to conclude that X and Y are dependent because the P-value > α. O B. No, do not reject Ho. There is sufficient evidence at the a= 0.05 level of significance to conclude that X and Y are dependent because the P-value <α. O C. No, do not reject Ho. There is not sufficient evidence at the a= 0.05 level of significance to conclude that X and Y are dependent because the P-value > α. O D. Yes, reject Ho. There is not sufficient evidence at the a= 0.05 level of significance to conclude that X and Y are dependent because the P-value < α. M₁₂₁ Y₂ X₁ 31 45 53 (33.50) (46.33) (49.18) X₂ X3 P 16 20 16 (13.50) (18.67) (19.82)
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