n=25 sample average= 96 sample standard deviation = 1.5. What is the lower bound of a 2-sided 95% confidence interval on the population standard deviation?
Solution :
Given that,
c = 0.95
s = 1.5
n = 25
At 95% confidence level the is ,
= 1 - 95% = 1 - 0.95 = 0.05
/ 2 = 0.05 / 2 = 0.025
/2,df = 0.025,24 = 39.36
and
1- /2,df = 0.975,24 = 12.40
2L = 2/2,df = 39.36
2R = 21 - /2,df = 12.40
The 95% confidence interval for is,
s (n-1) / /2,df < < s (n-1) / 1- /2,df
1.5( 25 - 1 ) / 39.36 < < 1.5( 25 - 1 ) / 12.40
1.17 < < 2.09
( 1.17 , 2.09)
The lower bound is 1.17
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