Does memory (mnemonic) training work? Number of words recalled before and after training for 10 subjects:$$ \begin{array} {l| {10*|c }} \text{Begin Training} & 204 & 393 & 391 & 265 & 326 & 220 & 423 & 342 & 480 & 464 \\ \hline \text{After Training} &223 & 412 & 402 & 285 & 353 & 243 & 443 & 340 & 582 & 440 \\ \hline \text{Difference} & 19 & 19 & 11 & 20 & 27 & 23 & 20 & -2 & 102 & 26 \end{array} $$Test $H_0: D=0$ versus $H_1:D>0$ at $\alpha=0.02$

$\bar{D}=26.5\quad s_D=27.82$

$t=\frac{26.5-0}{27.82/\sqrt{10}}= 3.012$ with $df=n-1=9$

$0.005<P-values<0.01 $. Reject $H_0$ and accept $H_1$. This sample provides enough evidence to claim that memory training works.

Does handling affect weight of birds? Here is data on the weight of birds before and after handling:$$ \begin{array} {l| {6*|c }} \text{At First Capture} & 28.3 & 39.4 & 18.6 & 33.6 & 75.4 & 49.6 \\ \hline \text{At Recapture} & 27.1 & 39.2 & 19.1 & 30.8 & 72.8 & 50.0 \\ \hline \text{Difference} & -1.2 & -0.2 & 0.5 & -2.8 & -3.4 & -0.4\end{array} $$Test $H_0: D=0$ versus $H_1:D<0$ at $\alpha=0.05$ level of significance.

$\bar{D}=-1.25\quad s_D=1.544$

$t=\frac{-1.25-0}{1.544/\sqrt{6}}= 1.983$ with $df=5$

$0.05<P-values<0.10 $. Fail to reject $H_0$. This sample does not provide enough evidence to claim that handling birds affects their weight.