2. The weights of piglets at birth, \(M \mathrm {~kg}\), are normally distributed \(\mathrm { N } \left( \mu , \sigma ^ { 2 } \right)\)
A random sample of 9 piglets is taken and their weights at birth, \(m \mathrm {~kg}\), are recorded. The results are summarised as
$$\sum m = 11.6 \quad \sum m ^ { 2 } = 15.2$$
Stating your hypotheses clearly, test at the 5\% level of significance
- whether or not the mean weight of piglets at birth is greater than 1.2 kg ,
- whether or not the standard deviation of the weights of piglets at birth is different from 0.3 kg .