8 It is known that the lifetime of a certain species of animal in the wild has mean 13.3 years. A zoologist reads a study of 50 randomly chosen animals of this species that have been kept in zoos. According to the study, for these 50 animals the sample mean lifetime is 12.48 years and the population variance is 12.25 years \(^ { 2 }\).

1. Test at the \(5 \%\) significance level whether these results provide evidence that animals of this species that have been kept in zoos have a shorter expected lifetime than those in the wild.
2. Subsequently the zoologist discovered that there had been a mistake in the study. The quoted variance of 12.25 years \({ } ^ { 2 }\) was in fact the sample variance. Determine whether this makes a difference to the conclusion of the test.
3. Explain whether the Central Limit Theorem is needed in these tests.