5. A new species of animal has been found on an uninhabited island. A zoologist wishes to investigate whether or not there is a difference in the mean weights of males and females of the species. She traps some of the animals and weighs them with the following results.
| Males (kg) | \(5 \cdot 3,4 \cdot 6,5 \cdot 2,4 \cdot 5,4 \cdot 3,5 \cdot 5,5 \cdot 0,4 \cdot 8\) |
| Females (kg) | \(4 \cdot 9,5 \cdot 0,4 \cdot 1,4 \cdot 6,4 \cdot 3,5 \cdot 3,4 \cdot 2,4 \cdot 5,4 \cdot 8,4 \cdot 9\) |
You may assume that these are random samples from normal populations with a common standard deviation of 0.5 kg .
- State suitable hypotheses for this investigation.
- Determine the \(p\)-value of these results and state your conclusion in context.