In order to perform diagnostics on the consistency of a labr

In order to perform diagnostics on the consistency of a labratory scale...

In order to perform diagnostics on the consistency of a laboratory scale, multiple measurements are taken using a single weight over the course of several days. Hie variance observed over 20 repeated measures is 248. Construct a 99% confidence interval on the measurement variance of this scale. (122.129.688.486) (11.051,26.239) (117.809.633.862) (174.034.413.213)

Solution

Confidence Interval
CI = (n-1) S^2 / ^2 right < ^2 < (n-1) S^2 / ^2 left
Where,
S^2 = Variance
^2 right = (1 - Confidence Level)/2
^2 left = 1 - ^2 right
n = Sample Size

Since aplha =0.01
^2 right = (1 - Confidence Level)/2 = (1 - 0.99)/2 = 0.01/2 = 0.005
^2 left = 1 - ^2 right = 1 - 0.005 = 0.995
the two critical values ^2 left, ^2 right at 19 df are 38.582 , 6.844
Variacne( S^2 )=248
Sample Size(n)=20
Confidence Interval = [ 19 * 248/38.582 < ^2 < 19 * 248/6.844 ]
= [ 4712/38.582 < ^2 < 4712/6.844 ]
= [ 122.129 , 688.486 ]