The manager of a lumber yard wants to assess the performance of a saw mill that cuts beams that are supposed to be 100 cm long. The manager takes a sample of 50 beams from the saw mill and measures their lengths.
The manager performs a 1 variance test to determine whether the standard deviation of the saw mill is different from 1.
Because the data does not appear to come from a normal distribution, the manager uses the confidence interval for the Bonett method. The 95% confidence interval shows that a likely range for the population standard deviation of the length of all beams from the saw mill is approximately 0.704 cm and 1.121 cm. Because the pvalue is greater then 0.05, the manager cannot conclude that the population standard deviation is different from 1.

σ: standard deviation of Length  The Bonett method is valid for any continuous distribution.  The chisquare method is valid only for the normal distribution. 


50  0.870943  0.758542  (0.70409, 1.12130)  (0.72753, 1.08531) 


Null hypothesis  H₀: σ = 1  Alternative hypothesis  H₁: σ ≠ 1 



Bonett    0.2755  ChiSquare  37.17  49  0.2154 

