Question

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. Y1 X1 X3 32 45 49 (32.72) (47.34) (45.94) 15 23 17 (14.28) 20.66) (20.06) Y2 (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: Hy = Ex and Hy = Ey H: Hy + Ex or Hy + Ey OB. Ho: The Y category and X category are dependent H,: The Y category and X category are independent. O C. Ho: The Y category and X category are independent. Hy: The Y category and X category are dependent. OD. Ho: The Y category and X category have equal proportions. H. The proportions are not equal. What is the P-value? P-value = (Round to three decimal places as needed.) 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 > a. OB. 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>a OC. 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 <a. OD. 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.

Answer 1

2=0.05 observed frequencie (is) Expected frequencies (540) X3 X3 32 49 17. X 7, 32.72 44.34 Y2 114.28 | 20,66 45.94 20.06 15 23 test statistic x² = ² 2 2 roij- Eij) 21 Eij = 162-32.72) 27+545-47.34727 +7 (49 45.94927 47 34 45.94 -|(15-14.28)27 @3-20,66)27 + (1+- 20.06)27 14.28 20.66 32.72 + 20.06 0.5184 14.28 10.5184 +5.4756 + g. 36367 + 32-72 27.34 45.94 5.4756 9. 3636 20.66 + + 20.06 -0.0158 +0.157 +0.0038 + 0.0363 + 0.2650 70.4668 (X² 1.103 Test that x and fare independent @ Ho: The category y and y category are independent H,: The y category and te category are dependent P d.fa co-1) (6-1) = (2-1) 3-D def rano of rows cano. of column 2

P-value = P (X7 d. f x²) - P(X²2 1.103) 1- P(x²2 < 1.103) = 1 - CHISG. DIST (1.103,2,1) 0.4239 using Excel P valve Decision Reject Ho if p valve ca Here prale - 0.576 x -0.05 Fail to reject Ho. Do not reject Ho. В. No, do not reject Ho. There is not sufficient evidence at the d=0.05 level of significance to conclude that X and Y are dependent because jovalve >