- A machine fills packets with almonds. The weight, in grams, of almonds in a packet is modelled by \(\mathrm { N } \left( \mu , \sigma ^ { 2 } \right)\). To check that the machine is working properly, a random sample of 10 packets is selected and unbiased estimates for \(\mu\) and \(\sigma ^ { 2 }\) are
$$\bar { x } = 202 \quad \text { and } \quad s ^ { 2 } = 3.6$$
Stating your hypotheses clearly, test, at the \(1 \%\) level of significance, whether or not the mean weight of almonds in a packet is more than 200 g .