5. Boxes of chocolates manufactured by Philippe have a mean weight of \(\mu\) grams and a standard deviation of \(\sigma\) grams. A random sample of 25 of these boxes are weighed. Using this sample, the unbiased estimate of \(\mu\) is 455 and the unbiased estimate of \(\sigma ^ { 2 }\) is 55 .

1. Test, at the \(5 \%\) level of significance, whether or not \(\sigma\) is greater than 6 . State your hypotheses clearly.
2. Test, at the \(5 \%\) level of significance, whether or not \(\mu\) is more than 450 .
3. State an assumption you have made in order to carry out the above tests.