A mayor in a large city claims that in one particularly depressed neighborhood, at least $20\%$ of all males between ages $18$ and $65$ are unemployed. A random sample of $120$ people from this population included twenty unemployed.

$($a$)$ Test the mayor$$s claim at a $5\%$ significance level.

$($b$)$ Calculate the power of the test.

$($c$)$ Plot the power curve from $3$b in R$.$

$($d$)$ Looking at the graph from $3$c$,$ for what values of p $($roughly$)$ is the power at least $0\mathrm{.}8?$ For those values of p$,$ what is the upper bound on the probability of Type II error?

$($e$)$ What$$s the upper bound on the power for p $>=0\mathrm{.}2?$

where do we get the $\mathrm{.}14$ here in answer to question c$?$ can someone please explain the concept of power. also explain the answer to question e $($c$)$ Here the power function plotted in excel looks

as follows; pictures.

$$ The three colvins correspond to the values of

$($ficre the Excel function Normal distribution

refurnis the lower$-$tail probabilities$)$:

$$ Column. $1$:$P_1$

Colvonn $2$;$\frac{0\mathrm{.}14-P_1}{\sqrt[\phantom{2}]{P_1\frac{1-P_1}{120}}}$

Column $3$ :

Power

$=F_z(\frac{0\mathrm{.}14-P_1}{\sqrt[\phantom{2}]{P_1\frac{1-P_1}{120}}})$

NoRmDIST umn $\{$:$2,0,1,1)/$