Final Answer:
The null hypothesis (H₀) is that the true proportion of car crashes occurring within 5 miles of the crashing person's home is 56% or less. The alternative hypothesis (H₁) is that the true proportion is more than 56%.
Step-by-step explanation:
In hypothesis testing, the null hypothesis (H₀) represents the status quo or a default assumption, while the alternative hypothesis (H₁) suggests a departure from this assumption. In this scenario, the null hypothesis posits that 56% or fewer car crashes occur within 5 miles of the crashing person's home. The alternative hypothesis contends that the true proportion of such crashes is greater than 56%.
The study Jill is skeptical about involves hypothesis testing to assess whether the reported 56% is a significant underestimation. To evaluate this, Jill collects a random sample of 156 crashes, finding that 97 occurred within 5 miles of the crashing person's home. To test the hypotheses, she would use statistical methods to determine the probability of obtaining a sample result as extreme as 97 out of 156 if the true proportion were 56% or less. If this probability is low (typically below a pre-defined significance level, such as 0.05), Jill may reject the null hypothesis in favor of the alternative, providing evidence that the true proportion is indeed more than 56%.
In summary, the null hypothesis assumes the reported proportion is accurate, and the alternative hypothesis challenges this, suggesting a higher proportion. Jill's sample and subsequent statistical analysis aim to determine if there's enough evidence to reject the null hypothesis and support Jill's skepticism about the reported crash proportion.