The Student Senate at a Local University Is About to Hold

question 28

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. Which of the following is the correct conclusion for the test at = 0.05?

• A) Reject H₀: p₁ = p₂ and therefore conclude that the proportions differ.
• B) Reject H₀: p₁ = p₂ and therefore do not conclude that the proportions differ.
• C) Do not reject H₀: p₁ = p₂ and therefore conclude that the proportions differ.
• D) Do not reject H₀: p₁ = p₂ and therefore do not conclude that the proportions differ.

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Definitions:

Random Selection

A method of selecting a sample from a population in a way that gives every member of the population an equal chance of being chosen.

Representative Sample

A subset of a population that closely mirrors the characteristics of the overall population, used in research to draw conclusions about the population as a whole.

Population

a group of individuals of the same species living in the same geographic area at the same time, capable of interbreeding.

Theoretical Perspectives

Frameworks or lenses through which scientists and researchers view, analyze, and interpret phenomena within a field of study.