Question

Calculate the two-sided 95% confidence interval for the population standard deviation (sigma) given that a sample of size n=8 yields a sample standard deviation of 7.96.

Answer 1

ANSWER:

Given that,

Calculate the two-sided 95% confidence interval for the population standard deviation (sigma) given that a sample of size n=8 yields a sample standard deviation of 7.96.

Sample size = n = 8

Sample standard deviation = s = 7.96

c = 95% = 95/100 = 0.95

= 1-c = 1-0.95 = 0.05

/2 = 0.05/2 = 0.025

1-(/2) = 1-(0.025) = 0.975

= = = 16.012764

= = = 1.689869

95% confidence interval for the population standard deviation (sigma)

(n-1) / < < (n-1) /

((8-1)*(7.96)^2) /16.012764 < < ((8-1)*(7.96)^2) /1.689869

27.698603439 < < 262.464841949

sqrt(27.698603439) < < sqrt(262.464841949)

5.262946269818836 < < 16.20076670867771

5.2629 < < 16.2008

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