A lab technician is tested for her consistency by making multiple measurements of the cholesterol level in one blood sample. The target precision is a standard deviation of $1.2 \mathrm { mg } / \mathrm { dL }$ or less. If 12 measurements are taken and the standard deviation is
$2.1 \mathrm { mg } / \mathrm { dL }$, is there enough evidence to support the claim that her standard deviation is greater than the target, at $\alpha = 0.01$ ?
A) No, since the $\chi ^ { 2 }$ test value $19.25$ is less than the critical value $26.217$.
B) Yes, since the $\chi ^ { 2 }$ test value $33.688$ is greater than the critical value $24.725$.
C) No, since the $\chi ^ { 2 }$ test value $19.25$ is less than the critical value $24.725$.
D) Yes, since the $\chi ^ { 2 }$ test value $33.688$ is greater than the critical value $26.217$.

Question

Quizplus · Accepted Answer

To determine if there's enough evidence to support the claim that the standard deviation is greater than the target, a chi-square test for variance can be used. The chi-square test statistic is calculated using the formula $\chi^2 = \frac{(n-1)s^2}{\sigma^2}$, where $n$ is the sample size, $s^2$ is the sample variance, and $\sigma^2$ is the population variance under the null hypothesis. Given $n = 12$, $s = 2.1 \mathrm{mg/dL}$, and $\sigma = 1.2 \mathrm{mg/dL}$, the test statistic can be calculated. The critical value for a chi-square test at $\alpha = 0.01$ with $n-1 = 11$ degrees of freedom needs to be looked up in a chi-square distribution table. Choice B indicates a test statistic ($33.688$) that is greater than the critical value ($24.725$), suggesting that there is enough evidence at the 0.01 level of significance to support the claim that the standard deviation of the measurements is greater than the target.

A Lab Technician Is Tested for Her Consistency by Making 1.2mg/dL1.2 \mathrm { mg } / \mathrm { dL }1.2mg/dL

A Lab Technician Is Tested for Her Consistency by Making $1.2 \mathrm { mg } / \mathrm { dL }$