Question

a lab technician is tested for her consistency by taking multiple measurements of cholesterol levels from the same blood sample. the target accuracy has an average of 2.78 or less with a standard deviation of 1.17. if the lab technician takes 16 measurements and the variance of the measurements in the sample is 2.45, does this provide enough evidence to reject the claim that the lab technicians accuracy is within the target accuracy? compute the value of the appropriate test statistic.

Explanation:

Step1: Identify the known values

We know that the sample size $n = 16$, the sample variance $s^{2}=2.45$, and the population - standard deviation $\sigma = 1.17$, so the population variance $\sigma^{2}=(1.17)^{2}=1.3689$.

Step2: Select the test - statistic formula

For testing a hypothesis about a population variance, we use the chi - square test - statistic formula $\chi^{2}=\frac{(n - 1)s^{2}}{\sigma^{2}}$.

Step3: Calculate the chi - square test - statistic

Substitute the values into the formula:
$\chi^{2}=\frac{(16 - 1)\times2.45}{1.3689}=\frac{15\times2.45}{1.3689}=\frac{36.75}{1.3689}\approx26.84$.

Answer:

The value of the appropriate test statistic is approximately $26.84$.