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 $\alpha = 0.01$.
$\begin{array}{cc}
\hline \text { Horseshoe Lake } & \text { Swan Lake } \
\hline \bar{X}_{1}=43.0 \mathrm{~cm} & \bar{X}_{2}=38.6 \mathrm{~cm} \
\sigma_{1}=3.2 \mathrm{~cm} & \sigma_{2}=2.4 \mathrm{~cm} \
n_{1}=30 & n_{2}=30
\end{array}$

Question

Quizplus · Accepted Answer

The Answer is

H _ { 0 } : \mu _ { 1 } = \mu _ { 2 } , H _ { 1 } : \mu _ { 1 } > \mu _ { 2 } ext { (claim) }

Critical Value:

2.33

Test value:

z = 6.02

Reject the null hypothesis since

6.02 > 2.33

.
There is enough evidence to support the claim that the water level in Horses Lake is further below normal than the water level in Swan Lake.

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

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