Question

A group of doctors is deciding whether or not to perform an operation. Suppose the null hypothesis, ${\mathrm{H}}_0$, is: the surgical procedure will go well. State the Type I and Type II errors in complete sentences.

Short answer

Type I error is the surgical procedure will go well, but the doctors don't think so

Type II error is the surgical procedure will not go well but the doctors think it will

Step-by-step solution

Introduction

A type I error is defined as rejecting the null hypothesis ,when it is true.

A type II error is characterized as failing to reject the null hypothesis when it is wrong.

A group of doctors is debating whether or not to carry out a procedure. $H_0$: The surgery will be successful.

Explanation

When running a hypothesis test, there are four possible results depending on whether the null hypothesis $H_0$is true (or untrue) and whether or not to reject it.

a. Wrong decision - When $H_0$is true, the decision is not to reject it.

b. Type I error - When $H_0$is true, the decision is to reject it.

c. Type II error - When $H_0$is false, the decision is not to dismiss it.

d. Power of the Test - When $H_0$is false, the decision is to reject $H_0$

Hence,

Type I error is the surgical procedure will go well, but the doctors don't think so

Type II error is the surgical procedure will not go well but the doctors think it will