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 twocategories. 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 = EyH₁: #Ex or μy # EyWhat range of P-values does the test statistic correspond to?The P-value isShould 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.M₁₂₁Y₂X₁31 45 53(33.50) (46.33) (49.18)X₂ X3 P16 20 16(13.50) (18.67) (19.82)

Introduction The chi-square test is a non-parametric test.

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

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.7: Probability

Problem 58E: What is meant by the sample space of an experiment?