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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 a previous analysis showed that 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 is 0.704 cm and 1.121 cm. A likely range for the population variance is 0.496 cm and 1.257 cm. Because the p-value is greater than 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. |
| N | StDev | Variance | 95% CI for σ using Bonett | 95% CI for σ using Chi-Square |
|---|---|---|---|---|
| 50 | 0.871 | 0.759 | (0.704, 1.121) | (0.728, 1.085) |
| Null hypothesis | H₀: σ = 1 |
|---|---|
| Alternative hypothesis | H₁: σ ≠ 1 |
| Method | Test Statistic | DF | P-Value |
|---|---|---|---|
| Bonett | — | — | 0.275 |
| Chi-Square | 37.17 | 49 | 0.215 |
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