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. 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 hypothesis tests must be performed to determine whether the percentages of supporting votes are different between the two incumbent candidates? A) A z test of two sample proportions with a zero hypothesized difference. B) A t test of two population proportions with a zero hypothesized difference. C) A z test of two population proportions with a zero hypothesized difference. D) A t test of two population proportions with a nonzero hypothesized difference.

Question

Quizplus · Accepted Answer

Since we are comparing two population proportions (proportions of supporting votes for the incumbent candidates representing women's and men's sports programs), we need to perform a z test (as opposed to a t test, which is used for comparing sample means). We are hypothesizing that there is no difference between the two proportions (i.e. a zero hypothesized difference), so our null hypothesis would be p₁ = p₂. Therefore, we need to use a z test of two population proportions with a zero hypothesized difference.

The Student Senate at a Local University Is About to Hold