Question

When a new drug is created, the pharmaceutical company must subject it to testing before receiving the necessary permission from the Food and Drug Administration (FDA) to market the drug. Suppose the null hypothesis is “the drug is unsafe.” What is the Type II Error?

a. To conclude the drug is safe when in, fact, it is unsafe.

b. Not to conclude the drug is safe when, in fact, it is safe.

c. To conclude the drug is safe when, in fact, it is safe.

d. Not to conclude the drug is unsafe when, in fact, it is unsafe.

Short answer

Type I error for the drug is safe: One thinks the drug is safe when, in fact, it really is not.

Type II error for the drug is not safe: One thinks the drug is not safe when, in fact, it really is.

Step-by-step solution

Introduction

Statistics main purpose is to verify or disprove a notion.

For example, you might conduct research and discover that a particular medicine is useful in the treatment of headaches.

No one will believe your findings if you can't repeat the experiment.

In statistical hypothesis testing, a type I error occurs when a null hypothesis is rejected when it is true.

The type II error arises when the null hypothesis is accepted even when it is false.

Explanation Part a

We are given $H_0$The drug is unsafe. Therefore, the null hypothesis state that the drug is unsafe.

Rejecting the null hypothesis $H_0$when it is true is defined as a Type I error.

The Type I error is: One thinks the drug is safe when, in fact, it really is not.

Failing to reject the null hypothesis when it is false is defined as a Type II error.

The Type II error is: One thinks the drug is not safe, when, in fact, it really is.

Hence, option a is incorrect.

Explanation Part b

Type II error occurs when the null hypothesis is accepted (not rejected) even when it is false. The Type II error is: One thinks the drug is not safe, when, in fact, it really is.

Since option b accepts the null hypothesis even when it is false.

Explanation Part c

The Type I error is: One thinks the drug is safe when, in fact, it really is not.

The Type II error is: One thinks the drug is not safe, when, in fact, it really is.

The option says that drug is safe even if it is actually safe, which defines none of the type I or type II error.

Hence, option c is incorrect.

Explanation Part d

The Type I error is: One thinks the drug is safe when, in fact, it really is not.

The Type II error is: One thinks the drug is not safe, when, in fact, it really is.

The option "d" says that drug is unsafe even if it is actually unsafe, which defines neither of the type I or type II error.

Hence, option d is incorrect.