Question

In a study of 11,000 car​ crashes, it was found that 5698 of them occurred within 5 miles of home​ (based on insurance company​ data). use a 0.01 significance level to test the claim that more than​ 50% of car crashes occur within 5 miles of home. use this information to answer the following questions.

a.Which of the following is the hypothesis test to be​ conducted.

A. H₀ :p = 0.5
H₁ :p > 0.5

B. H₀ :p ≠ 0.5
H₁ :p = 0.5

C. H₀ :p = 0.5
H₁ :p ≠ 0.5

D. H₀ :p < 0.5
H₁ :p = 0.5

E. H₀ :p > 0.5
H₁ :p = 0.5

Answer 1

The correct hypothesis test for checking if more than 50% of car crashes occur within 5 miles of home is H0: p = 0.5 vs. H1: p > 0.5.

Step-by-step explanation:

To test the claim that more than 50% of car crashes occur within 5 miles of home, we need to formulate the correct set of hypotheses.

The appropriate hypothesis test to conduct in this situation is option A, with the null hypothesis (H0) being that the proportion of crashes within 5 miles of home is 0.5 (or 50%) and the alternative hypothesis (H1) being that the proportion is greater than 0.5. This can be mathematically represented as:

• H0: p = 0.5
• H1: p > 0.5

Based on the insurance company data, which shows 5698 out of 11,000 crashes occurring within 5 miles, we will calculate the test statistic and compare it with the critical value or calculate the p-value and compare it with the significance level (alpha) of 0.01 to make a decision about the hypotheses.