Question

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?

Answer 1

`H_(0): \mu \geq 240\text{ cholestrol level}\\H_A: \mu < 240\text{ cholestrol level}`

Explanation:

We are given the following in the question:

Population mean, μ = 240

Sample mean,
`\bar{x}` = 250

Sample size, n = 100

Alpha, α = 0.05

Sample standard deviation, s = 40

First, we design the null and the alternate hypothesis

`H_(0): \mu \geq 240\text{ cholestrol level}\\H_A: \mu < 240\text{ cholestrol level}`

Interpretation:

The null hypothesis state that sample belongs to the population and has a cholesterol level of greater than equal to 240 whereas the alternate hypothesis states that the sample does not belong to the population and have a cholesterol level of less than 240.