Question

A random sample of n=7 observations are drawn from a normal population with mean and variance σ^2. The mean and variance of the sample are 1.45 and 2.07 respectively. Calculate a 90% confidence interval for the population standard deviation.

Answer 1

((n − 1)SP/x. 1/2) <04 ((n − 1)SP/xi-o -0.1/2

$(( 7-1 ) \, 2.07 / 12.5916 ) < \sigma^2 < ((7-1)\, 2.07 / 1.6354 )$
$\chi^2$ (0.1/2, 7 - 1 ) = 12.5916
$\chi^2$ (1 - 0.1/2, 7 - 1) ) = 1.6354
Lower Limit = 0.9932
Upper Limit = 2.7558
90% Confidence interval is ( 0.9932 , 2.7558 )
( 0.9932 < σ < 2.7558 )