Question

A lab technician is tested for her consistency by taking multiple measurements of cholesterol levels from the same blood sample. The target accuracy in the past has been 2.5 or less with a standard deviation of 1.15. 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? At the a = .05 level of significance, what is your conclusion?

A. Reject H0. At the alpha= .05 level of significance, there is not enough evidence to support the claim that this technician’s true average is less than the target accuracy.

B. Reject H0 . At the \f$\alpha \f$ = .05 level of significance, there is enough evidence to support the claim that this technician’s average is less than the target accuracy.

C. Cannot determine

D. Do not reject H0. At the \f$\alpha \f$ = .05 level of significance there is not sufficient evidence to suggest that this technician’s true average is less than the target accuracy.

Answer 1

using minitab>stat>basic stat>onw variance

we have

Test and CI for One Variance

Method

Null hypothesis σ-squared = 1.3225
Alternative hypothesis σ-squared < 1.3225

The chi-square method is only for the normal distribution.
The Bonett method cannot be calculated with summarized data.

Statistics

N StDev Variance
16 1.48 2.20

95% One-Sided Confidence Intervals

Upper
Bound
for Upper Bound
Method StDev for Variance
Chi-Square 2.13 4.54

Tests

Test
Method Statistic DF P-Value
Chi-Square 24.95 15 0.949

since p-value of chi-square stat is 0.949 which is greater than 0.05 so do not reject Ho

option d is true

D. Do not reject H0. At the a = .05 level of significance there is not sufficient evidence to suggest that this technician’s true average is less than the target accuracy.