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 1.4 mg/dL or less. If 16 measurements are taken and the standard deviation is 2.1 mg/dL, is there enough evidence to support the claim that her standard deviation is greater than the target, at = .01? A) Yes, since the χ² test value 33.750 is greater than the critical value 32.000. B) No, since the χ² test value 22.50 is less than the critical value 30.578. C) Yes, since the χ² test value 33.750 is greater than the critical value 30.578. D) No, since the χ² test value 22.50 is less than the critical value 32.000.

Question

Quizplus · Accepted Answer

To test whether the standard deviation is greater than the target, we use a chi-square test for the variance with a null hypothesis that the variance is equal to or less than the target variance. The test statistic is calculated as:

χ^2 = (n-1)*s^2/σ^2

where n is the sample size, s is the sample standard deviation, and σ is the target standard deviation. Under the null hypothesis, this test statistic follows a chi-square distribution with (n-1) degrees of freedom.

In this case, n = 16, s = 2.1, and σ = 1.4. Substituting these values into the formula, we get:

χ^2 = (16-1)*2.1^2/1.4^2 = 33.75

The critical value for a chi-square distribution with 15 degrees of freedom (corresponding to a significance level of 0.01) is 30.578. Since the calculated χ^2 value of 33.75 is greater than the critical value of 30.578, we reject the null hypothesis and conclude that there is enough evidence to support the claim that the standard deviation is greater than the target. Therefore, the best choice is C.

A Lab Technician Is Tested for Her Consistency by Making