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. identify the type of test.
a left tailed
b right tailed
c two - tailed

Explanation:

In hypothesis testing, the type of test (left - tailed, right - tailed, or two - tailed) is determined by the alternative hypothesis. Here, the research question is whether runners have a lower blood glucose level. The null hypothesis \(H_0:\mu = 100\) (where \(\mu\) is the population mean of blood glucose level) and the alternative hypothesis \(H_1:\mu<100\). For a one - sided alternative hypothesis of the form \(H_1:\mu <\mu_0\) (in this case \(\mu_0 = 100\)), the test is left - tailed. A left - tailed test looks at the left tail of the normal distribution to find the rejection region. A right - tailed test (\(H_1:\mu>\mu_0\)) would look at the right tail, and a two - tailed test (\(H_1:\mu
eq\mu_0\)) would look at both tails.

Answer:

A. Left Tailed