College

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 below.

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 [tex]p_1[/tex] and [tex]p_2[/tex] 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. [tex]H_0: p_1 \leq p_2[/tex], [tex]H_a: p_1 > p_2[/tex].

B. [tex]H_0: p_1 \geq p_2[/tex], [tex]H_a: p_1 < p_2[/tex].

C. [tex]H_0: p_1 = p_2[/tex], [tex]H_a: p_1 \neq p_2[/tex].

D. [tex]H_0: p = p_0[/tex], [tex]H_a: p \neq p_0[/tex].

Answer :

The competing hypotheses to determine whether the percentages of supporting votes are different between the two incumbent candidates are: a. H0: p1 ≤ p2, Ha: p1 > p2.

Null Hypothesis (H0): This represents the statement we want to test and assume to be true in the absence of evidence to the contrary. The null hypothesis (H0) states that there is no difference between the proportions of supporting votes for the incumbent candidates representing women's and men's sports programs.

Alternative Hypothesis (Ha): This represents the statement we want to disprove or find evidence for against the null hypothesis. The alternative hypothesis (Ha) states that the proportion of supporting votes is greater for the women's incumbent candidate than for the men's incumbent candidate.