Question

With the statistics n=27, x¯¯¯=75.0, and s2=144.0, find to construct a 95% confidence interval estimate of σ

______ σ ________

With the statistics n=27n=27, x¯¯¯=75.0x¯=75.0, and s2=144.0s2=144.0, find to construct a 95% confidence interval estimate of σ2.

_____ <σ2<_____

Answer 1

Solution :

Given that,

Point estimate = s² = 144.0

²_R = ²_/2,df = 41.923

²_L = ²_{1 - /2,df} = 13.844

The 95% confidence interval for ² is,

(n - 1)s² / ²_/2 < ² < (n - 1)s² / ²_{1 - /2}

(26)(144.0) / 41.923 < ² < (26)(144\.0) / 13.844

9.5 < ² < 16.4

Point estimate = s² = 144.0

²_R = ²_/2,df = 41.923

²_L = ²_{1 - /2,df} = 13.844

The 95% confidence interval for is,

(n - 1)s² / ²_/2 < < (n - 1)s² / ²_{1 - /2}

(26)(144.0) / 41.923 < < (26)(144.0) / 13.844

89.3 < < 270.4