Example of 1 Variance
main topic     interpreting results     session command     see also 

You are a quality control inspector at a factory that builds high precision parts for aircraft engines, including a metal pin that must measure 15 inches in length. Safety laws dictate that the variance of the pins' length must not exceed 0.001in2. Previous analyses determined that pin length is normally distributed. You collect a sample of 100 pins and measure their length in order to conduct a hypothesis test and create a confidence interval for the population variance.

1    Open the worksheet AIRPLANEPIN.MTW.

2    Choose Stat > Basic Statistics > 1 Variance.

3    Choose One or more samples, each in a column and enter 'Pin length'.

4   Check Perform hypothesis test and choose Hypothesized variance.

5    In Value, enter 0.001.

6    Click Options. Under Alternative hypothesis, choose Variance < hypothesized variance.

7    Click OK in each dialog box.

Session window output

Test and CI for One Variance: Pin length

 

 

Method

 

Null hypothesis         σ-squared = 0.001

Alternative hypothesis  σ-squared < 0.001

 

The chi-square method is only for the normal distribution.

The Bonett method is for any continuous distribution.

 

 

Statistics

 

Variable      N   StDev  Variance

Pin length  100  0.0267  0.000715

 

 

95% One-Sided Confidence Intervals

 

                        Upper Bound   Upper Bound

Variable    Method        for StDev  for Variance

Pin length  Chi-Square       0.0303      0.000919

            Bonett           0.0296      0.000878

 

 

Tests

 

                             Test

Variable    Method      Statistic  DF  P-Value

Pin length  Chi-Square      70.77  99    0.014

            Bonett              —   —    0.004

Interpreting the results

Because the data comes from a normally distributed population, refer to the chi-square method. The p-value for the one-sided hypothesis test is 0.014. This value is sufficiently low to reject the null hypothesis and conclude that the variance of pin length is less than 0.001. You can further hone your estimate of the population variance by considering the 95% upper bound, which provides a value that the population variance is likely to be below. From this analysis, you should conclude that the variance of pin length is small enough to meet specifications and ensure passenger safety.