Question

Calculate the two-sided 95% confidence interval for the population standard deviation (sigma) given that a sample of size n=13 yields a sample standard deviation of 5.75.

Your answer:
	4.32 < sigma < 1.68
	5.26 < sigma < 6.85
	7.28 < sigma < 0.12
	6.62 < sigma < 10.89
	4.56 < sigma < 8.31
	5.18 < sigma < 18.58
	4.56 < sigma < 8.54
	5.71 < sigma < 15.54
	7.20 < sigma < 7.52
	4.12 < sigma < 9.49

Answer 1

Sample Size,   n=   13
Sample Standard Deviation,   s=   5.7500
Confidence Level,   CL=   0.95
      
      
Degrees of Freedom,   DF=n-1 =    12
alpha,   α=1-CL=   0.05
alpha/2 ,   α/2=   0.025
Lower Chi-Square Value=   χ²1-α/2 =   4.404
Upper Chi-Square Value=   χ²α/2 =   23.337

confidence interval for std dev is       
lower bound= √[(n-1)s²/χ²α/2] =   √(12*5.75² / 23.3367)=   4.12
      
      
upper bound= √[(n-1)s²/χ²1-α/2] =   √(12*5.75² / 4.4038)=   9.49
      

4.12 < sigma < 9.49