Many cities around the United States are installing LED streetlights, in part to combat crime by improving visibility after dusk. An urban police department claims that the proportion of crimes committed after dusk will fall below the current level of 0.84 if LED streetlights are installed. Specify the null and alternative hypotheses to test the police department's claim. A) H₀: p = 0.84 and H_A: p ≠ 0.84 B) H₀: p 0.84 D) H₀: p ≥ 0.84 and H_A: p

Question

Many cities around the United States are installing LED streetlights, in part to combat crime by improving visibility after dusk. An urban police department claims that the proportion of crimes committed after dusk will fall below the current level of 0.84 if LED streetlights are installed. Specify the null and alternative hypotheses to test the police department's claim. A) H₀: p = 0.84 and H_A: p ≠ 0.84 B) H₀: p < 0.84 and H_A: p ≥ 0.84 C) H₀: p ≤ 0.84 and H_A: p > 0.84 D) H₀: p ≥ 0.84 and H_A: p < 0.84

Quizplus · Accepted Answer

The null hypothesis (H0) typically states that there is no effect or no difference, so it would assert that the proportion of crimes committed after dusk is at least 0.84 (p ≥ 0.84), assuming no improvement with LED lights. The alternative hypothesis (Ha) is what the police department claims, which is that the proportion of crimes after dusk will fall below the current level of 0.84 (p < 0.84) with the installation of LED streetlights.

Many Cities Around the United States Are Installing LED Streetlights