The Student Senate at a Local University Is About to Hold

Multiple Choice

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. Use a 5% level of significance. Which of the following is(are) critical value(s) of the appropriate test?

A) 1.645
B) 1.960
C) -1.645 and +1.645
D) -1.960 and ±1.960