EJC Hypothesis Testing Tutorial Q11

The mass of a bag of salted cashew nuts is normally distributed, with standard deviation \(1.6\)g.

The manufacturer claims that the population mean of the mass of a bag of salted cashew nuts is \(100\)g.

A customer claimed that the bags of salted cashew nuts have been lighter in recent purchases, so the factory quality control manager decided to investigate. He sampled \(n\) bags of salted cashew nuts and found that their mean weight was \(99.4\)g. He performed a \(1\%\) significance test and concluded that the customer’s claim was not valid.

Find the largest possible value of \(n\).