Question

it is known that blood glucose level is normally distributed with a mean of 100 mg/dl and a σ = 4.5. you want to determine if runners have a lower blood glucose level. you take a sample of 25 runners and calculate a sample mean of 98. for this study the alternate hypothesis would state:
(a) h₁: μ < 100
(b) h₀: μ = 100
(c) h₀: μ = 98
(d) h₁: μ < 98

Explanation:

The null hypothesis \(H_0\) is a statement of no - difference or equality. The alternative hypothesis \(H_1\) is the claim we are trying to find evidence for. In this case, we want to determine if runners have a lower blood glucose level. The population mean (from the known distribution) is \(\mu = 100\) (this is the value we are comparing against). The alternative hypothesis for a lower - tailed test (since we are looking for a lower blood glucose level) is \(H_1:\mu<100\). Option B and C are null hypotheses (\(H_0\) is about equality, and we are not testing against the sample mean of 98 for the null in the context of the problem's setup). Option D is incorrect because we are comparing to the known population mean of 100, not the sample mean of 98.

Answer:

A. \(H_1:\mu < 100\)