When estimating y = β₀ + β₁x₁ + β₂x₂+ β₃x₃ + ε, you wish to test H₀: β₁= β₂versus H_A: β₁≠ β₂. The value of the test statistic is F_(1,30) = 7.75 and its associated p-value is 0.0092. At the 1% significance level, the conclusion is to ________. A) reject the null hypothesis; we cannot conclude that the influence of x₁ on y is different from the influence of x₂ on y. B) reject the null hypothesis; we can conclude that the influence of x₁ on y is different from the influence of x₂ on y. C) not reject the null hypothesis; we can conclude that the influence of x₁ on y is different from the influence of x₂ on y. D) not reject the null hypothesis; we cannot conclude that the influence of x₁ on y is different from the influence of x₂ on y.

Question

Quizplus · Accepted Answer

The small p-value (0.0092) suggests strong evidence against H₀, and we can reject it at the 1% level of significance. Since the alternative hypothesis H_A: β₁≠ β₂ is the complement of H₀, we accept it. Therefore, we can conclude that the influence of x₁ on y is different from the influence of x₂ on y.

When Estimating Y = β0 + β1x1 + β2x2

When Estimating Y = β₀ + β₁x₁ + β₂x₂