91Ó°ÊÓ

Significance test

$\begin{array}{r}{H}_0:p=0.10\\ H_a:p<0.10\end{array}$

Significance level =$5\%$and power =role="math" localid="1652846359690" $0.64$

Given,

$\begin{array}{r}{H}_0:p=0.10\\ H_a:p<0.10\end{array}$

power = $0.64=64\%$

alternative p = $0.08$

Hence the "power =$0.64$" means rejecting the null hypothesis if it's false.

Given,

$\begin{array}{r}{H}_0:p=0.10\\ H_a:p<0.10\end{array}$

power = $0.64=64\mathrm{\%}$

alternative p = $0.08$

Hence to build the power, then you require more data about the information, which can be gotten by expanding the quantity of estimation. Accordingly, we make more measurements to increase the power.

Given,

If we decide to use$\mathrm{Î\pm }=0.01$in place of $\mathrm{Î\pm }=0.05$, with no other changes in the test then the power will decrease as the probability of type I error decreases and the probability of type II error increases.

Now,

$\text{Power}=1−\mathrm{β}$(probability of type II error)

Hence power decreases as$\mathrm{β}$increases.

If we shift your interest to the alternative p= $0.07$with no other changes then the power will increase as it is further from the null hypothesis p =$0.10$

Hence the power increases.