2 The heights of a certain species of animal have been found to have mean 65.2 cm and standard deviation 7.1 cm . A researcher suspects that animals of this species in a certain region are shorter on average than elsewhere. She takes a large random sample of \(n\) animals of this species from this region and finds that their mean height is 63.2 cm . She then carries out an appropriate hypothesis test.

1. She finds that the value of the test statistic \(z\) is - 2.182 , correct to 3 decimal places.
   (a) Stating a necessary assumption, calculate the value of \(n\).
   (b) Carry out the hypothesis test at the \(4 \%\) significance level.
2. Explain why it was necessary to use the Central Limit theorem in carrying out the test.