Find the \(P \%=(1-\alpha) 100 \%\) interval estimates \(\widehat{I_{\alpha}^{\mu}}, \widehat{I_{\alpha}^{\sigma}}\) (use that \(\sigma=1 / \sqrt{\tau}\) ) and \(\widehat{I_{\alpha}^{+}} ; \sigma\) is unknown.

(a) \(\alpha=0.1\). We have 29 observations with average \(\bar{x}=8.2069\) and sample standard deviation \(s_{x}=1.68818\).

(b) \(P \%=98 \%\). We have 398 observations with average \(\bar{x}=29.6886\) and sample standard deviation \(s_{x}=4.72427\).

(c) You have examined mechanical wear on a certain flooring, and want to find a \(98 \%\) confidence interval for the mean wear. You examined 8 floors, and measured wear depths of respectively 49.3, 65.8, 55.5, 54.4, 58.7, 61.7, 63.2, \(57.8 \mu \mathrm{m}\).