Question

Listed below is the sodium content in milligrams (mg) for 5 of Wendy’s burgers. This data was obtained from their web site. Determine the confidence interval for the true standard deviation of sodium content at the 95% level of confidence. Assume the data are independent random samples and are normally distributed. The answers are in milligrams.

1540     1250     1230     1400     1440

Answer 1

Sample Size,   n=   5
Sample Standard Deviation,   s=   131.0343
Confidence Level,   CL=   0.95
      
      
Degrees of Freedom,   DF=n-1 =    4
alpha,   α=1-CL=   0.05
alpha/2 ,   α/2=   0.025
Lower Chi-Square Value=   χ²1-α/2 =   0.4844
Upper Chi-Square Value=   χ²α/2 =   11.1433
      
95%   confidence interval for variance is  
lower bound= (n-1)s²/χ²α/2 =   4*131.0343² / 11.1433=   6163.352
      
upper bound= (n-1)s²/χ²1-α/2 =   4*131.0343² / 0.4844=   141778.218
95%   confidence interval for variance is  

confidence interval for std dev is       
lower bound=   √(lower bound variance)=   78.507
      
      
upper bound=   √(upper bound of variance=   376.534

      

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