A Conservationist Suspects That the Water Level in Horseshoe Lake $\alpha = 0.01$

Essay

A conservationist suspects that the water level in Horseshoe Lake has been affected more by the current drought than the water level in Swan Lake, so he measures how far the water level is below normal each day in June. The data are normally distributed. Test his hypothesis at $\alpha = 0.01$ .
$\begin{array}{cc}\hline \text { Horseshoe Lake } & \text { Swan Lake } \\\hline \bar{X}_{1}=43.0 \mathrm{~cm} & \bar{X}_{2}=38.6 \mathrm{~cm} \\\sigma_{1}=3.2 \mathrm{~cm} & \sigma_{2}=2.4 \mathrm{~cm} \\n_{1}=30 & n_{2}=30\end{array}$