# Example of 1 Variance

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.

1. Open the sample data, BeamLength.MTW.
2. Choose Stat > Basic Statistics > 1 Variance.
3. From the drop-down list, select One or more samples, each in a column and enter Length.
4. Select Perform hypothesis test and enter 1 in Value.
5. Click OK.

## Interpret the results

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.

### Test and CI for One Variance: Length

Method 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.
Descriptive Statistics 95% CI for σ 95% CI for σ using N StDev Variance using Bonett Chi-Square 50 0.871 0.759 (0.704, 1.121) (0.728, 1.085)
Test Null hypothesis H₀: σ = 1 Alternative hypothesis H₁: σ ≠ 1
Test Method Statistic DF P-Value Bonett — — 0.275 Chi-Square 37.17 49 0.215
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