Why is important to perform a hypothesis test about a standard deviation?
Precision is as important as accuracy.
Knowing the mean of a population is important, but just as important is the accuracy and precision of your measurement. If you design a machine to fill 20 oz. soda bottles, you may find that the actual sample mean is
But margins of error are calculated from standard deviations, not the mean. How do you know the margin of error is 0.3 oz and not 3.0 oz? If you can't predict your standard deviation within a given interval, i.e. if your standard deviation is not accurate, your margin of error will be inaccurate.
It's important to not only estimate the population mean, but having a low margin of error for the standard deviation will help you make that prediction with a lower amount of error.