The following table contains the number of successes and failures for three categories of a variable. Test whether the proportions are equal for each category at the α = 0.01 level of significance. Failures Successes Category 1 Category 2 80 58 73 65 State the hypotheses. Choose the correct answer below. Category 3 D 45 41 A. Ho: P₁ P2 = P3 H₁: At least one of the proportions is different from the others. B. Ho: ₁=E₁ and μ₂ = ₂ and μ3 = E3 H₁: At least one mean is different from what is expected. C. Ho: The categories of the variable and success and failure are dependent. H₁: The categories of the variable and success and failure are independent. What is the P-value? D. Ho: The categories of the variable and success and failure are independent. H₁: The categories of the variable and success and failure are dependent. (Round to three decimal places as needed.)

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