Q.30 - The Practice of Statistics for AP

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 Il error for the particular alternative value of the parameter at which she computed the power is

(a) 0.01

(b) 0.10

(c) 0.89

(d) 0.90

(c) 0.99

Step-by-Step Solution

Answer

The probability that the researcher will commit a Type Il error for the particular alternative value of the parameter at which she computed the power is option b. $0.10$

Step 1: Introduction

A type I error is a sort of issue that happens during the speculation testing process when an invalid theory is dismissed, despite the fact that it is precise and ought not to be dismissed.

Step 2: Explanation

Given,

A researcher plans to conduct a significance test at the $\alpha =0.01$significance level.

power = $0.90$

Probabilty of type II error = $1-$power

$$\begin{gathered} =1-0.90 \\ =0.10 \end{gathered}$$

Hence option b. $0.10$ is correct