Question

question 2
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. calculate the test statistic (z - score).

Explanation:

Step1: Recall the formula for z - score

The formula for the z - score in a one - sample z - test for the mean is \(z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}\), where \(\bar{x}\) is the sample mean, \(\mu\) is the population mean, \(\sigma\) is the population standard deviation, and \(n\) is the sample size.

Step2: Identify the values

Given \(\bar{x} = 98\), \(\mu=100\), \(\sigma = 4.5\), and \(n = 25\).

Step3: Calculate the denominator

First, calculate \(\frac{\sigma}{\sqrt{n}}\). Since \(n = 25\), \(\sqrt{n}=5\). Then \(\frac{\sigma}{\sqrt{n}}=\frac{4.5}{5}=0.9\)

Step4: Calculate the numerator

The numerator is \(\bar{x}-\mu=98 - 100=- 2\)

Step5: Calculate the z - score

Substitute the values into the z - score formula: \(z=\frac{-2}{0.9}\approx - 2.22\)

Answer:

\(-2.22\)