4. A random sample of 15 tomatoes is taken and the weight \(x\) grams of each tomato is found. The results are summarised by \(\sum x = 208\) and \(\sum x ^ { 2 } = 2962\).
- Assuming that the weights of the tomatoes are normally distributed, calculate the \(90 \%\) confidence interval for the variance \(\sigma ^ { 2 }\) of the weights of the tomatoes.
- State with a reason whether or not the confidence interval supports the assertion \(\sigma ^ { 2 } = 3\).