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 $\left(FDA\right)$to market the drug. Suppose the null hypothesis is "the drug is unsafe." What is the $TypeII$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

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

$TypeII$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 

• Rejecting the null hypothesis $H_0$when it is true is defined as a $TypeI$error.

If the $H_0$is "The drug is unsafe", than $TypeI$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 role="math" localid="1650038358356" $TypeII$error.

Therefore $TypeII$error is:

• One thinks the drug is not safe, when, in fact, it really is.