Assume we are interested in determining whether the proportion of voters planning to vote for candidate A (define this proportion as $\pi$_A) is less than the proportion of voters planning to vote for candidate B (define this proportion as $\pi$_B) using the contrary position as the null hypothesis.The correct set of hypotheses for testing here is A)H₀: $\pi$ _A - $\pi$_B

Question

Assume we are interested in determining whether the proportion of voters planning to vote for candidate A (define this proportion as $\pi$_A) is less than the proportion of voters planning to vote for candidate B (define this proportion as $\pi$_B) using the contrary position as the null hypothesis.The correct set of hypotheses for testing here is A)H₀: $\pi$ _A - $\pi$_B < 0; H_a: $\pi$_A - $\pi$_B $\ge$ 0 B)H₀: $\pi$_A - $\pi$_B $\ge$ 0; H_a: $\pi$_A - $\pi$_B < 0 C)H₀: $\pi$_A - $\pi$_B = 0; H_a: $\pi$_A - $\pi$_B $\neq$ 0 D)H₀: $\pi$_A - $\pi$_B $\le$ 0; H_a: $\pi$_A - $\pi$_B > 0 E)none of the above

Quizplus · Accepted Answer

The null hypothesis should state there is no difference or the opposite of what we are trying to prove, which in this case is that the proportion of voters for candidate A is greater than or equal to the proportion for candidate B. The alternative hypothesis should reflect what we are trying to prove, which is that the proportion for candidate A is less than the proportion for candidate B. Option B correctly sets the null hypothesis as the proportion of voters for A minus the proportion for B being greater than or equal to 0, and the alternative hypothesis as this difference being less than 0.

Assume We Are Interested in Determining Whether the Proportion of Voters