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. (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= 0.01 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. Ho: The Y category and X category are dependent. H₁: The Y category and X category are independent. OD. Ho: HxEx and μly = Ey H₁: HxEx or Hy Ey Y₁ Y₂ X₂ X₁ 33 45 (34.82) (46.43)(45.75) X3 49 18 23 18 (16.18) (21.57) (21.25)

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What is the P-value?
P-value =
Should the null hypothesis be rejected?
(Round to three decimal places as needed.)
O A. Yes, reject Ho. There is not sufficient evidence at the α = 0.01 level of significance to conclude that X and Y are dependent because the P-value < x.
B. Yes, reject Ho. There is not sufficient evidence at the x = 0.01 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 α = 0.01 level of significance to conclude that X and Y are dependent because the P-value > α.
O D. No, do not reject Ho. There is sufficient evidence at the x = 0.01 level of significance to conclude that X and Y are dependent because the P-value < α.
Transcribed Image Text:What is the P-value? P-value = Should the null hypothesis be rejected? (Round to three decimal places as needed.) O A. Yes, reject Ho. There is not sufficient evidence at the α = 0.01 level of significance to conclude that X and Y are dependent because the P-value < x. B. Yes, reject Ho. There is not sufficient evidence at the x = 0.01 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 α = 0.01 level of significance to conclude that X and Y are dependent because the P-value > α. O D. No, do not reject Ho. There is sufficient evidence at the x = 0.01 level of significance to conclude that X and Y are dependent because the P-value < α.
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.
(a) Compute the value of the chi-square test statistic.
2
x² =
=
(Round to three decimal places as needed.)
(b) Test the hypothesis that X and Y are independent at the α = 0.01 level of significance.
O A. Ho: The Y category and X category have equal proportions.
H₁:
: The proportions are not equal.
B. Ho: The Y category and X category are independent.
H₁: The Y category and X category are dependent.
O C. Ho: The Y category and X category are dependent.
H₁: The Y category and X category are independent.
O D. Ho: x = Ex and μy = Ey
Hy
H₁: Hx #Ex or Hy # Ey
Y₁
Y₂
X₂
X3
45 49
X₁
33
(34.82) (46.43)(45.75)
18
18
(16.18) (21.57) (21.25)
23
□
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. (a) Compute the value of the chi-square test statistic. 2 x² = = (Round to three decimal places as needed.) (b) Test the hypothesis that X and Y are independent at the α = 0.01 level of significance. O A. Ho: The Y category and X category have equal proportions. H₁: : The proportions are not equal. B. Ho: The Y category and X category are independent. H₁: The Y category and X category are dependent. O C. Ho: The Y category and X category are dependent. H₁: The Y category and X category are independent. O D. Ho: x = Ex and μy = Ey Hy H₁: Hx #Ex or Hy # Ey Y₁ Y₂ X₂ X3 45 49 X₁ 33 (34.82) (46.43)(45.75) 18 18 (16.18) (21.57) (21.25) 23 □
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