# 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. Open the 1 Variance dialog box.
• Mac: Statistics > 1-Sample Inference > Variance
• PC: STATISTICS > One Sample > Variance
3. From the drop-down list, select Sample data in a column and enter Length.
4. Select Perform hypothesis test and enter 1 in Hypothesized standard deviation.
5. Click OK.

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.

 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
 N StDev Variance 95% CI for σ Bonett 95% CI for σ Chi-Square 50 0.870943 0.758542 (0.70409, 1.12130) (0.72753, 1.08531)
 Test
 Null hypothesis H₀: σ = 1 Alternative hypothesis H₁: σ ≠ 1
 Method Test Statistic DF P-Value Bonett 0.2755 Chi-Square 37.17 49 0.2154
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