Question

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 1.2 mg/dL or less. If 12 measurements are taken and the standard deviation is 1.8 mg/dL, is there enough evidence to support the claim that her standard deviation is greater than the target, at = .01? (Show the answers to all 5 steps of the hypothesis test.)

Answer 1

Explanation:

Given precision is a standard deviation of s=1.8, n=12, target precision is a standard deviation of σ=1.2

The test hypothesis is

H_o:σ <=1.2

Ha:σ > 1.2

The test statistic is

chi square =
`((n-1)s^2)/(\sigma^2)`

=
`((12-1)1.8^2)/(1.2^2)`

=24.75

Given a=0.01, the critical value is chi square(with a=0.01, d_f=n-1=11)= 3.05 (check chi square table)

Since 24.75 > 3.05, we reject H_o.

So, we can conclude that her standard deviation is greater than the target.