2023 JPJC P2 Q6

The production manager of a badminton racket company wishes to check that the mean mass of the badminton rackets produced is \(800\)g as stated in the design specifications. The population standard deviation of the badminton rackets is \(20\)g. He carries out a hypothesis test on a large sample of \(n\) badminton rackets. The sample mean mass is \(807\)g and the null hypothesis is rejected at the \(2\%\) level of significance.

1. Use an algebraic method to find the least value of \(n\) that will support this conclusion.[6]
2. Explain whether there is a need for the production manager to know anything about the population distribution of the masses of the badminton rackets.[1]