3 The weights in kg of male otters in a large river system are known to be Normally distributed with mean 8.3 and standard deviation 1.8. A researcher believes that weights of male otters in another river are higher because of what he suspects is better availability of food. The researcher records the weights of a random sample of 9 male otters in this other river. The sum of these 9 weights is 83.79 kg .

1. In this question you must show detailed reasoning. You should assume that:
   • the weights of otters in the other river are Normally distributed,
   • the standard deviation of the weights of otters in the other river is also 1.8 kg .
   Show that a test at the \(5 \%\) significance level provides sufficient evidence to conclude that the mean weight of male otters in the other river is greater than 8.3 kg .
2. Explain whether the result of the test suggests that the weights are higher due to better availability of food.
3. If the standard deviation of the weights of otters in the other river could not be assumed to be 1.8 kg , name an alternative test that the researcher could carry out to investigate otter weights.
4. Explain why, even if a test at the \(5 \%\) significance level results in the rejection of the null hypothesis, you cannot be sure that the alternative hypothesis is true.