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:

Prior Probabilities

Initial probabilities used in Bayesian analysis, representing beliefs about probabilities before new evidence is taken into account.

Joint Probabilities

The probability of two events occurring together and at the same point in time.

Union Probabilities

The probability of the occurrence of at least one of two or more events.

Likelihood Probabilities

Refers to the use of probabilities to express the plausibility of parameter values given a sample of data, central in statistical inference.