2. The time, \(t\) hours, that a typist can sit before incurring back pain is modelled by \(\mathrm { N } \left( \mu , \sigma ^ { 2 } \right)\). A random sample of 30 typists gave unbiased estimates for \(\mu\) and \(\sigma ^ { 2 }\) as shown below.
$$\hat { \mu } = 2.5 \quad s ^ { 2 } = 0.36$$
- Find a 95\% confidence interval for \(\sigma ^ { 2 }\)
- State with a reason whether or not the confidence interval supports the assertion that \(\sigma ^ { 2 } = 0.495\)