Q.44 - 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 0.54 to detect that p=0.07. Explain what this means.

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

Step-by-Step Solution

Answer

a. Type I error - rejecting the null hypothesis even if its incorrect and Type II error- the null hypothesis even if it's false

b. The probability of rejecting the null hypothesis is $0.54$

c. choose a greater sample size and choose a greater significance level.

Step 1: Introduction

A type I error is the mixed up dismissal of a genuine null hypothesis, while a  type II error is the inability to dismiss an null hypothesis that is not true.

Step 2: Explanation Part (a)

Type I error here is concluding that under $10\%$ of patients who take the new medication will experience sickness yet it is misleading. The outcome of this error might prompt patient passing.

Type Il error: Fail to dismiss a bogus invalid hypothesis. It is otherwise called bogus negative.

Type II error here is concluding that it is at least $10\%$ of patients who take the new medication will experience sickness when it is under $10\%$. The result of this error is not serious as action will be taken to diminish the patient's discomfort.

Step 3: Explanation Part (b)

The probability of rejecting the null hypothesis is $0.54$ indicating the probability of dismissing the null hypothesis when p = $0.07$.

Step 4: Explanation Part (c)

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

i. choose a greater sample size 

ii. choose a greater significance level.