Hypothesis Testing - One-Tailed Hypothesis Tests

A distributor for health products claimed that his slimming pills could help women reduce their masses. An experiment was carried out to test his claim. \(80\) women whose original masses were \(60\) kg were randomly chosen and they took the slimming pills for a period of time. Their masses were then taken and recorded. Their mean mass was found to be \(59.5\) kg.

Denote the population standard deviation of the masses by \(\sigma \) kg. A statistical test was carried out at \(5\%\) level of significance and it was concluded that the slimming pills help to reduce the women’s masses. Find the range of values of \(\sigma \).