Een bewering over de standaarddeviatie testen

Correct pricing of gold requires an accurate scale, and its accuracy is achieved by reducing the standard deviation of the mean weight.

Consider an example where a company claims that they have significantly reduced the standard deviation of their scales from 0.005 g to 0.003 g tested over 30 individual units.

To test this claim, a hypothesis test is conducted where the null hypothesis states that the old and improved models have an equal standard deviation. The alternative hypothesis states that the improved model is more accurate and has a significantly smaller standard deviation than the old model.

Testing the hypothesis requires the sample statistic to be converted to the Χ² statistic as follows.

Here, the critical region at a 0.05 significance level falls at the left tail of the curve.

Observe that the Χ² value calculated from the sample falls within it.

Also, the P-value obtained using the left-tailed test is less than 0.05.

So, the improved model proves significantly more accurate than the old model based on the test result.