Question

A researcher plans to conduct a significance test at the $\alpha =0.01$ significance level. She designs her study to have a power of $0.90$ at a particular alternative value of the parameter of interest. The probability that the researcher will commit a Type II error for the particular alternative value of the parameter she used is

$$\begin{gathered} a.0.01. \\ b.0.10. \\ c.0.89. \\ d.0.90. \\ e.0.99. \end{gathered}$$

Short answer

The correct option is (b) $0.10$

Step-by-step solution

Given information

$\alpha =0.01$

Explanation

The most appropriate response to the given statement "A researcher intends to conduct a significance test with a significance level of $\alpha =0.01$. She plans for a power of $0.90$for a certain alternative value of the parameter of interest in her investigation. She computed the power at a certain alternative value of the parameter, the risk of the researcher making a Type II error is $0.10$"

Power is calculated in this case as,

$$\begin{gathered} 1-P(Type2error)P(Type2error)+Power=1 \\ P(Type2error)=1-Power \\ P(Type2error)=1-0.90 \\ P(Type2error)=0.10 \end{gathered}$$