Solution
= Solution
The same affine transformation of the <normal distribution> gives
$$
\boxed{W_n\mid\delta=\delta^*\sim N\left(\frac{\sqrt n\delta^*}{\sigma},1\right).}
$$
Its <variance> stays one while its mean moves positively. This is the exact alternative distribution used to calculate <statistical power>. The square, if used instead, has a <noncentral chi-squared distribution> with one degree of freedom and noncentrality $n(\delta^*)^2/\sigma^2$.