EJC Hypothesis Testing Tutorial Q12

An alpaca breeder wants to produce fleece which is extremely fine. In 2008, his herd had mean fineness \(22.3\) microns with standard deviation \(\sigma \) microns. The standard deviation remains relatively constant over time. In 2012, a sample of \(80\) alpacas from the herd was randomly selected, and the mean fineness was \(21.2\) microns.

Find the range of values of the standard deviation which will indicate a significant change in mean fineness at the \(5%\) two-tailed significance test.