Q.43 - The Practice of Statistics for AP

Question

(a) Describe a Type I error and a Type II error in this setting, and explain the consequences of each.

(b) The test has a power of 0.75 to detect that p= 0.45. Explain what this means.

(c) Identify two ways to increase the power in part (b).

Step-by-Step Solution

Answer

a. type I error- null hypothesis rejected even if it's correct and type II error- null hypothesis is not rejected even if it's not correct 

b. The true proportion is $0.45$

c. increase the level of significance and increase the sample size.

Step 1: Introduction

The null hypothesis is a run of the mill factual hypothesis which proposes that no factual relationship and importance exists in a bunch of given single noticed variables, between two arrangements of noticed information and estimated peculiarities.

Step 2: Explanation Part (a)

Type I error- null hypothesis rejected even if it's correct 

Type II error- null hypothesis is not rejected even if it's not correct  

Step 3: Explanation Part (b)

$0.75$ is the probability of rejecting the null hypothesis and the true proportion is $0.45$.

Step 4: Explanation Part (c)

The two ways to increase the power in part (b) are-

i. increase the level of significance 

ii. increase the sample size.