QUESTION 12 In a sample of 100 people who have had strokes, the average cholesterol level was 250 with a standard deviation of 40. In order to test the hypothesis (at the \( 5 \% \) level of significance) that the average cholesterol level of people who have had strokes was at least 240 , what is the null and alternative hypotheses? \( H_{0}: \mu=240, H_{A}: \mu \neq 240 \) \( H_{0}: \mu \leq 240, H_{A}: \mu>240 \) \( H_{0}: \mu \geq 240, H_{A}: \mu<240 \) \( H_{0}: p \geq 240, H_{A}: p<240 \) \( H_{0}: p \leq 240, H_{A}: p>240 \) \( H_{0}: p=240, H_{A}: p \neq 240 \) \( H_{0}: \bar{p}=240, H_{A}: \bar{p} \neq 240 \) \( H_{0}: \bar{p} \geq 240, H_{A}: \bar{p}<240 \) \( H_{0}: \bar{p} \leq 240, H_{A}: \bar{p}>240 \) \( H_{0}: \bar{X} \leq 250, H_{A}: \bar{X}>250 \) \( H_{0}: \bar{X} \geq 250, H_{A}: \bar{X}<250 \) \( H_{0}: \bar{X}=250, H_{A}: \bar{X} \neq 250 \)

In hypothesis testing, we typically articulate the null and alternative hypotheses to investigate the claim made about a population parameter. In your case, since you want to test if the average cholesterol level of people who have had strokes is at least 240, the correct choices would be \( H_{0}: \mu \geq 240 \) and \( H_{A}: \mu < 240 \). This setup allows you to explore the possibility that the average may indeed dip below the threshold you’re concerned about. To add some spice to your statistical adventures, consider that the concept of hypothesis testing has its roots in the early 20th century, pioneered by statistics wizards like Ronald A. Fisher and Jerzy Neyman. They developed this elegant framework to help researchers make decisions based on data, creating a lasting impact on fields ranging from medicine to psychology and beyond! It’s fascinating how these principles still resonate in today's data-driven world.