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 p-value 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 chi-square method is valid only for the normal distribution.
H₀: σ = 1
H₁: σ ≠ 1