In the last mayoral election in a large city,47% of the adults over the age of 65 voted Republican.A researcher wishes to determine if the proportion of adults over the age of 65 in the city who plan to vote Republican in the next mayoral election has changed.Let p represent the proportion of the population of all adults over the age of 65 in the city that plan to vote Republican in the next mayoral election.In terms of p,the researcher should test which of the following null and alternative hypotheses?

A) H₀: p = 0.47 vs.H_a: p < 0.47
B) H₀: p = 0.47 vs.H_a: p  0.47
C) H₀: p = 0.47 vs.H_a: p > 0.47

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Lauren Gamino · Accepted Answer

Final Answer : B, Explanation :  The researcher wishes to determine if the proportion of adults over the age of 65 in the city who plan to vote Republican in the next mayoral election has changed. This implies a one-tailed test, as the researcher is only interested in whether the proportion has decreased from the previous election. Therefore, the null hypothesis should state that p = 0.47, and the alternative hypothesis should state that p < 0.47. Choice B is the correct hypothesis test that satisfies these conditions.

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