Question

it is known that blood glucose level is normally distributed with a mean of 100 mg/dl and a \\( \sigma=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 null hypothesis would state:
a \\( h_1: \mu<100 \\)
b \\( h_0: \mu = 100 \\)
c \\( h_0: \mu = 98 \\)
d \\( h_1: \mu<98 \\)

Explanation:

The null hypothesis \(H_0\) is a statement of no difference or no effect. In hypothesis testing for a population mean \(\mu\), when the known population mean is given (here \(\mu = 100\) mg/dl), the null hypothesis is formulated as \(H_0:\mu=\) the known population mean value. Options A and D are alternative hypotheses (denoted by \(H_1\)), and option C uses the sample mean (98) instead of the population mean (100) which is incorrect for the null hypothesis.

Answer:

B. \(H_0:\mu = 100\)