- A nutritionist studied the levels of cholesterol, \(X \mathrm { mg } / \mathrm { cm } ^ { 3 }\), of male students at a large college. She assumed that \(X\) was distributed \(\mathrm { N } \left( \mu , \sigma ^ { 2 } \right)\) and examined a random sample of 25 male students. Using this sample she obtained unbiased estimates of \(\mu\) and \(\sigma ^ { 2 }\) as \(\hat { \mu }\) and \(\hat { \sigma } ^ { 2 }\)
A \(95 \%\) confidence interval for \(\mu\) was found to be \(( 1.128,2.232 )\)
- Show that \(\hat { \sigma } ^ { 2 } = 1.79\) (correct to 3 significant figures)
- Obtain a \(95 \%\) confidence interval for \(\sigma ^ { 2 }\)