A mayor is concerned about the percentage of city residents who express disapproval of his job performance. His political committee pays for a newspaper ad, hoping that it will keep the disapproval rate below $12 \%$. They will use a follow-up poll to assess the ad's effectiveness. The correct null and alternative hypotheses for testing this polls effectiveness are A) $H _ { 0 } : p = 0.12 , H _ { A } : p 0.12$ B) $H _ { 0 } : p 0.12 , H _ { A } : p = 0.12$ C) $H _ { 0 } : p 0.12 , H _ { A } : p

Question

A mayor is concerned about the percentage of city residents who express disapproval of his job performance. His political committee pays for a newspaper ad, hoping that it will keep the disapproval rate below $12 \%$. They will use a follow-up poll to assess the ad's effectiveness. The correct null and alternative hypotheses for testing this polls effectiveness are A) $H _ { 0 } : p = 0.12 , H _ { A } : p > 0.12$ B) $H _ { 0 } : p > 0.12 , H _ { A } : p = 0.12$ C) $H _ { 0 } : p > 0.12 , H _ { A } : p < 0.12$ D) $H _ { 0 } : p = 0.12 , H _ { A } : p < 0.12$ E) $H _ { 0 } : p < 0.12 , H _ { A } : p = 0.12$

Quizplus · Accepted Answer

The null hypothesis ($H_0$) typically represents the status quo or a situation of no change, which in this case is the disapproval rate being at $12\%$, hence $p = 0.12$. The alternative hypothesis ($H_A$) represents the outcome the mayor's committee hopes to achieve with the newspaper ad, which is to lower the disapproval rate below $12\%$, hence $p < 0.12$.

A Mayor Is Concerned About the Percentage of City Residents 12%12 \%12%

A Mayor Is Concerned About the Percentage of City Residents $12 \%$