Respuesta :
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. [tex]\sigma_1^2 =1.2[/tex]
The variance of the measurements in the sample is 2.2 i.e. [tex]\sigma_2^2=2.2[/tex]
According to question,
We state the null and alternative hypotheses,
Null hypothesis [tex]H_o : \text{var}^2 \geq 1.2[/tex]
Alternative hypothesis [tex]H_a : \text{var}^2<1.2[/tex]
We claim the alternative hypothesis.
2) Compute the value of the appropriate test statistic.
Using Chi-square,
[tex]\chi =\frac{(n-1)\sigma_2^2}{\sigma_1^2}[/tex]
[tex]\chi =\frac{(16-1)(2.2)}{(1.2)}[/tex]
[tex]\chi =\frac{(15)(2.2)}{1.2}[/tex]
[tex]\chi =\frac{33}{1.2}[/tex]
[tex]\chi =27.5[/tex]
Therefore, The value of the appropriate test statistic is 27.5.
