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# Examples - Inference on the variance of a population

A consumer group is investigating whether there is to little soda in cans from a certain soda factory. It is important that the filling process in the factory is stable, that is the variance is not higher than 10 ml , so that there is not many bottles with too much or too little soda. To investigate this an experiment was performed where a random sample of 30 bottles was taken and the standard deviation calculated to, . It can be assumed that the soda level follows a normal distribution. Test the hypothesis that the variance is higher than 10 ml . Use .

1. We would like to test a hypothesis regarding the variance of a normal distribution.

2. 3. The hypotheses are:      4. The test statistic is:  , = 10. 5. = 42.56. We reject the null hypothesis if . We see that .
6. We cannot reject the null hypothesis so we cannot conclude that the variance is larger than 10 ml .

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