The student senate at a local university is about to hold elections.A representative from the women's sports program and a representative from the men's sports program must both be elected.Two candidates,an incumbent and a challenger,are vying for each position and early polling results are presented next.A hypothesis test must be performed to determine whether the percentages of supporting votes are different between the two incumbent candidates.In a sample of 100 voters,67 said that they would vote for the women's incumbent candidate.In a separate sample of 100 voters,55 said they would vote for the men's incumbent candidate.Let p₁ and p₂ be the proportions of supporting votes for the incumbent candidates representing women's and men's sports programs,respectively.Which of the following are the competing hypotheses to determine whether the percentages of supporting votes are different between the two incumbent candidates? A) H₀: p = p₀ ,H_A: p ≠ p₀ B) H₀: p₁= p₂ ,H_A: p₁≠ p₂ C) H₀: p₁≤ p₂ ,H_A: p₁ p₂ D) H₀: p₁≥ p₂ ,H_A: p₁

Question

The student senate at a local university is about to hold elections.A representative from the women's sports program and a representative from the men's sports program must both be elected.Two candidates,an incumbent and a challenger,are vying for each position and early polling results are presented next.A hypothesis test must be performed to determine whether the percentages of supporting votes are different between the two incumbent candidates.In a sample of 100 voters,67 said that they would vote for the women's incumbent candidate.In a separate sample of 100 voters,55 said they would vote for the men's incumbent candidate.Let p₁ and p₂ be the proportions of supporting votes for the incumbent candidates representing women's and men's sports programs,respectively.Which of the following are the competing hypotheses to determine whether the percentages of supporting votes are different between the two incumbent candidates? A) H₀: p = p₀ ,H_A: p ≠ p₀ B) H₀: p₁= p₂ ,H_A: p₁≠ p₂ C) H₀: p₁≤ p₂ ,H_A: p₁> p₂ D) H₀: p₁≥ p₂ ,H_A: p₁< p₂

Quizplus · Accepted Answer

The competing hypotheses should be in terms of the proportions of supporting votes for the incumbent candidates representing women's and men's sports programs, which are represented by p₁ and p₂, respectively. Therefore, option A is incorrect as it uses only one parameter p for both incumbents. Option C is incorrect as it uses inequalities which do not make sense in this context. Option D is also incorrect as it uses inequalities in the wrong direction. Option B correctly sets up the competing hypotheses as H₀: p₁= p₂ and H_A: p₁≠ p₂.

The Student Senate at a Local University Is About to Hold