Question

The following sample of weights was taken from 9 cans of soda off the assembly line. Construct the 80% confidence interval for the population standard deviation for all cans of soda that come off the assembly line. Round your answers to two decimal places. 14.5,14.7,14.3,14.3,14.6,15.1,15.3,15.1,14.4

Answer 1

s = √(Σ(X- x̅ )²/(n-1) ) =0.3775
n=   9
Confidence level=   0.80

Degrees of Freedom,   DF=n-1 =    8
alpha,   α=1-CL=   0.2
alpha/2 ,   α/2=   0.1
Lower Chi-Square Value=   χ²_1-α/2 =   3.4895
Upper Chi-Square Value=   χ²_α/2 =   13.3616

confidence interval for variance is      
lower bound=   (n-1)s²/χ²_α/2 =   0.09
      
      
upper bound=   (n-1)s²/χ²_1-α/2 =   0.33
      

confidence interval for std dev is       
lower bound=   √(lower bound variance)=   0.29
      
      
upper bound=   √(upper bound of variance=   0.57