Questions: Identify the type I error and the type II error that corresponds to the given hypothesis. The proportion of people who write with their left hand is equal to 0.23 . Which of the following is a type I error? A. Reject the claim that the proportion of people who write with their left hand is 0.23 when the proportion is actually different from 0.23 . B. Fail to reject the claim that the proportion of people who write with their left hand is 0.23 when the proportion is actually different from 0.23 . C. Fail to reject the claim that the proportion of people who write with their left hand is 0.23 when the proportion is actually 0.23 . D. Reject the claim that the proportion of people who write with their left hand is 0.23 when the proportion is actually 0.23 .

Identify the type I error and the type II error that corresponds to the given hypothesis.
The proportion of people who write with their left hand is equal to 0.23 .

Which of the following is a type I error?
A. Reject the claim that the proportion of people who write with their left hand is 0.23 when the proportion is actually different from 0.23 .
B. Fail to reject the claim that the proportion of people who write with their left hand is 0.23 when the proportion is actually different from 0.23 .
C. Fail to reject the claim that the proportion of people who write with their left hand is 0.23 when the proportion is actually 0.23 .
D. Reject the claim that the proportion of people who write with their left hand is 0.23 when the proportion is actually 0.23 .

Transcript text: Identify the type I error and the type II error that corresponds to the given hypothesis. The proportion of people who write with their left hand is equal to 0.23 . Which of the following is a type I error? A. Reject the claim that the proportion of people who write with their left hand is 0.23 when the proportion is actually different from 0.23 . B. Fail to reject the claim that the proportion of people who write with their left hand is 0.23 when the proportion is actually different from 0.23 . C. Fail to reject the claim that the proportion of people who write with their left hand is 0.23 when the proportion is actually 0.23 . D. Reject the claim that the proportion of people who write with their left hand is 0.23 when the proportion is actually 0.23 .

Solution

Solution Steps

Step 1: Understanding Type I and Type II Errors

In hypothesis testing, we define two types of errors:

Type I Error (\( \alpha \)): This occurs when we reject the null hypothesis (\( H_0 \)) when it is actually true. In this context, it means rejecting the claim that the proportion of people who write with their left hand is \( 0.23 \) when it is indeed \( 0.23 \).
Type II Error (\( \beta \)): This occurs when we fail to reject the null hypothesis when it is actually false. Here, it means failing to reject the claim that the proportion of people who write with their left hand is \( 0.23 \) when it is actually different from \( 0.23 \).

Step 2: Identifying the Errors

Based on the definitions:

The option that describes a Type I Error is:
- D: Reject the claim that the proportion of people who write with their left hand is \( 0.23 \) when the proportion is actually \( 0.23 \).
The option that describes a Type II Error is:
- B: Fail to reject the claim that the proportion of people who write with their left hand is \( 0.23 \) when the proportion is actually different from \( 0.23 \).