Question

The average low-density lipoprotein (LDL) cholesterol level of adult males is 142 milligrams per deciliter. You want to determine whether the true mean male LDL cholesterol level is higher than the average. You decide to pull a random sample of 10 adult males and measure their LDL cholesterol level. You find the sample mean is 145.3 milligrams per deciliter and the standard deviation is 5.39 milligrams per deciliter. What are the test statistic and the p-value? (2 points)

Answer 1

Test statistic = 1.94

P-value = 0.0421

Explanation:

We are given the following in the question:

Population mean, μ = 142 milligrams per deciliter

Sample mean,
`\bar{x}` = 145.3 milligrams per deciliter

Sample size, n = 10

Alpha, α = 0.05

Sample standard deviation, s = 5.39 milligrams per deciliter

First, we design the null and the alternate hypothesis

`H_(0): \mu = 142\text{ milligrams per deciliter}\\H_A: \mu > 142\text{ milligrams per deciliter}`

We use one-tailed t test to perform this hypothesis.

Formula:

`t_(stat) = \displaystyle\frac{\bar{x} - \mu}{(s)/(√(n)) }`

Putting all the values, we have

`t_(stat) = \displaystyle(145.3 - 142)/((5.39)/(√(10)) ) = 1.934`

We can calculate the p-value as:

P-value = 0.0421