Question

Study more! The significance test in Exercise $76$yields a P-value of $0.0622$.

(a) Describe a Type I and a Type II error in this setting. Which type of error could you have made in Exercise $76$? Why?

(b) Which of the following changes would give the test a higher power to detect $\mu =120$minutes: using $\alpha =0.01$or $\alpha =0.10$? Explain.

Short answer

a. Type II error since we failed to reject $H_0$.

b. both $\alpha =0.01and\alpha =0.1$give the higher power.

Step-by-step solution

Given information

The significance test in Exercise $76$yields a P-value of $0.0622$.

Explanation (part a)

Type I error: experts conclude that student study hours has a higher mean yield when it actually doesn’t.

Type II error: experts conclude that there is a mean difference in yields when, in fact,

student study hours has a higher mean yield.

Type II error since we failed to reject $H_0$.

Explanation (part b)

$z\left(s\right)$ test statistics is:

$$\begin{gathered} z\left(s\right)=(x-\mu ₀)/s/\surd n \\ z\left(s\right)=-30/8.22 \\ z\left(s\right)=-3.65 \end{gathered}$$

p-value for that $z\left(s\right)$ $p-value=0$

Then for $\alpha =0.01or0.1;p-value<0.01or0.1$

We are in the rejection region we need to reject $H₀$. Therefore, both localid="1650893185130" $\alpha =0.01and\alpha =0.1$give the higher power.