In: Statistics and Probability
The following sample of lengths was taken from 8 nails off the assembly line. Construct the 90% confidence interval for the population variance for all nails that come off the assembly line. Round your answers to two decimal places.
19.3,19.1,19.6,19.7,19.1,19.2,19.0,19.0
Lower Endpoint: ??? and Upper Endpoint: ???
Solution :
Given that,
19.3,19.1,19.6,19.7,19.1,19.2,19.0,19.0
Point estimate = s2 = 0.07
n = 8
Degrees of freedom = df = n - 1 = 8 - 1 = 7
At 90% confidence level the
2 value is ,
The 95% confidence interval for
2 is,
(n - 1)s2 /
2
/2
<
2 < (n - 1)s2 /
21 -
/2
7 * 0.07 / 14.067 <
2 < 7 * 0.07 / 2.167
Lower endpoint = 0.04
Upper endpoint = 0.23
( , )