Question

A lab technician is tested for her consistency by taking multiple measurements of cholesterol levels from the same blood sample. The target accuracy is a variance in measurements of 1.2 or less. If the lab technician takes 16 measurements and the variance of the measurements in the sample is 2.2, does this provide enough evidence to reject the claim that the lab technician’s accuracy is within the target accuracy? Compute the value of the appropriate test statistic

Answer 1

Answer and Explanation:

Given : A lab technician is tested for her consistency by taking multiple measurements of cholesterol levels from the same blood sample.

The target accuracy is a variance in measurements of 1.2 or less. If the lab technician takes 16 measurements and the variance of the measurements in the sample is 2.2.

To find :

1) Does this provide enough evidence to reject the claim that the lab technician’s accuracy is within the target accuracy?

2)Compute the value of the appropriate test statistic ?

Solution :

1) n=16 number of sample

The target accuracy is a variance in measurements of 1.2 or less i.e. $\sigma_1^2 =1.2$

The variance of the measurements in the sample is 2.2 i.e. $\sigma_2^2=2.2$

According to question,  

We state the null and alternative hypotheses,

Null hypothesis $H_o : \text{var}^2 \geq 1.2$

Alternative hypothesis $H_a : \text{var}^2$

We claim the alternative hypothesis.

2) Compute the value of the appropriate test statistic.

Using Chi-square,

$\chi =\frac{(n-1)\sigma_2^2}{\sigma_1^2}$

$\chi =\frac{(16-1)(2.2)}{(1.2)}$

$\chi =\frac{(15)(2.2)}{1.2}$

$\chi =\frac{33}{1.2}$

$\chi =27.5$

Therefore, The value of the appropriate test statistic is 27.5.