A lab technician is tested for her consistency by making mul

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 1.5 mg/dL or less. If 18 measurements are taken and the standard deviation is 1.9 mg/dL, is there enough evidence to support the claim that her standard deviation is greater than the target, at = .01?

Solution

Let o be the standard deviation

Ho: o=1.5 (i.e. null hypothesis)

Ha: o>1.5 (i.e. alternative hypothesis)

The test statistic is

chisqurae= (n-1)*s^2/o^2

=(18-1)*1.9^2/1.5^2

=27.28

The degree of freedom =n-1=18-1=17

It is right-tailed test.

Given a=0.01, the critical value of chisquare with 0.99 and df=17 is 33.41 (from chisquare table)

Since 27.28 is less than 33.41, we do not reject the null hypothesis.

So we can not conclude that her standard deviation is greater than the target