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Sagot :
A 95% two-sided confidence interval is 0.46 < a <0.31 .
The formula for confidence interval for population standard deviation is,
[tex]s\sqrt{\frac{n-1}{X^{2} _{1-a/2,n-1} } }[/tex] < a < [tex]s\sqrt{\frac{n-1}{X^{2} _{a/2,n-1} } }[/tex]
Given in question,
Significance level, a = 1 - 0.95
= 0.05
Sample size, n = 51
Sample standard deviation, s = 0.37
By using chi-square distribution table, we get
[tex]X^{2} _{1-a/2,n-1}[/tex] = [tex]X^{2} _{0.975,50}[/tex]
= 32.36
[tex]X^{2} _{a/2,n-1}[/tex] = [tex]X^{2} _{0.025,50}[/tex]
= 71.42
Confidence interval for population standard deviation is :
[tex]0.37\sqrt{\frac{50}{32.36} }[/tex] < a < [tex]0.37\sqrt{\frac{50}{71.42} }[/tex]
0.45992018426 < a < 0.30958278534
Hence, a 95% two-sided confidence interval is 0.46 < a <0.31 .
To learn more about confidence interval here:
https://brainly.com/question/24131141
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