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: p1 ≤ p2, Ha: p1 > p2.b. H0: p1 ≥ p2, Ha: p1 < p2.c. H0: p1 = p2, Ha: p1 ≠ p2.d. H0: p = p0, Ha: p ≠ p0.

Answer 1

Answer: H0: p1 ≤ p2, Ha: p1 > p2

Explanation:

According to the information obtained, we can say that the hypothesis that determines that the percentages of support votes are different between the two incumbent candidates is as follows

H0: p1 ≤ p2, Ha: p1> p2

where the null hypothesis represents the difference between proportions