The table to the right contains observed values and expected values in parentheses for tw two categories. Use the table to complete parts (a) and (b) below. OB. H,: The Y category and X category have equal proportions. H,: The proportions are not equal. OC. Ho: The Y category and X category are dependent. H,: The Y category and X category are independent. OD. Ho: -E, and y =E, H,: H E, or H, E, %3D What is the P-value? P-value = =(Round to three decimal places as needed.) Enter your answer in the answer box and then click Check Answer.

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The table 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.

Categories:

- Variable X: 
  - \( X_1, X_2, X_3 \)

- Variable Y: 
  - \( Y_1, Y_2 \)

Observed and Expected Values:

\[
\begin{array}{c|c|c|c}
 & X_1 & X_2 & X_3 \\
\hline
Y_1 & 32\ (35.39) & 44\ (44.42) & 51\ (47.19) \\
Y_2 & 19\ (15.61) & 20\ (19.58) & 17\ (20.81) \\
\end{array}
\]

Hypotheses:

- Option B:
  - \( H_0 \): The Y category and X category have equal proportions.
  - \( H_1 \): The proportions are not equal.

- Option C:
  - \( H_0 \): The Y category and X category are dependent.
  - \( H_1 \): The Y category and X category are independent.

- Option D:
  - \( H_0 \): \(\mu_x = E_x\) and \(\mu_y = E_y\)
  - \( H_1 \): \(\mu_x \neq E_x\) or \(\mu_y \neq E_y\)

Question:

What is the P-value?

P-value = [ ] (Round to three decimal places as needed.)

Enter your answer in the answer box and then click Check Answer.
Transcribed Image Text:The table 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. Categories: - Variable X: - \( X_1, X_2, X_3 \) - Variable Y: - \( Y_1, Y_2 \) Observed and Expected Values: \[ \begin{array}{c|c|c|c} & X_1 & X_2 & X_3 \\ \hline Y_1 & 32\ (35.39) & 44\ (44.42) & 51\ (47.19) \\ Y_2 & 19\ (15.61) & 20\ (19.58) & 17\ (20.81) \\ \end{array} \] Hypotheses: - Option B: - \( H_0 \): The Y category and X category have equal proportions. - \( H_1 \): The proportions are not equal. - Option C: - \( H_0 \): The Y category and X category are dependent. - \( H_1 \): The Y category and X category are independent. - Option D: - \( H_0 \): \(\mu_x = E_x\) and \(\mu_y = E_y\) - \( H_1 \): \(\mu_x \neq E_x\) or \(\mu_y \neq E_y\) Question: What is the P-value? P-value = [ ] (Round to three decimal places as needed.) Enter your answer in the answer box and then click Check Answer.
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