$5 \%$ of trucks of a certain model have needed new engines after being driven between 0 and 100 miles. The manufacturer hopes that the redesign of one of the engine's components has solved this problem. The correct null and alternative hypotheses for testing this redesign are A) $H _ { 0 } : p 0.05 , H _ { A } : p = 0.05$ D) $H _ { 0 } : p = 0.05 , H _ { A } : p 0.05$

Question

$5 \%$ of trucks of a certain model have needed new engines after being driven between 0 and 100 miles. The manufacturer hopes that the redesign of one of the engine's components has solved this problem. The correct null and alternative hypotheses for testing this redesign are A) $H _ { 0 } : p < 0.05 , H _ { A } : p = 0.05$ B) $H _ { 0 } : p < 0.05 , H _ { A } : p > 0.05$ C) $H _ { 0 } : p > 0.05 , H _ { A } : p = 0.05$ D) $H _ { 0 } : p = 0.05 , H _ { A } : p < 0.05$ E) $H _ { 0 } : p = 0.05 , H _ { A } : p > 0.05$

Quizplus · Accepted Answer

The null hypothesis ($H_0$) typically represents the status quo or a statement of no effect, which in this case is that 5% of trucks need new engines ($p = 0.05$). The alternative hypothesis ($H_A$) represents what the manufacturer hopes to prove, that the redesign has decreased the proportion of trucks needing new engines, hence $p < 0.05$.

5%5 \%5% Of Trucks of a Certain Model Have Needed New Engines

$5 \%$ Of Trucks of a Certain Model Have Needed New Engines