Question

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 0.15. Which of the following is a type I​ error? A. Fail to reject the claim that the proportion of people who write with their left hand is 0.15 when the proportion is actually different from 0.15. B. Reject the claim that the proportion of people who write with their left hand is 0.15 when the proportion is actually different from 0.15. C. Fail to reject the claim that the proportion of people who write with their left hand is 0.15 when the proportion is actually 0.15. D. Reject the claim that the proportion of people who write with their left hand is 0.15 when the proportion is actually 0.15. Which of the following is a type II​ error? A. Fail to reject the claim that the proportion of people who write with their left hand is 0.15 when the proportion is actually 0.15. B. Fail to reject the claim that the proportion of people who write with their left hand is 0.15 when the proportion is actually different from 0.15. C. Reject the claim that the proportion of people who write with their left hand is 0.15 when the proportion is actually different from 0.15. D. Reject the claim that the proportion of people who write with their left hand is 0.15 when the proportion is actually 0.15.

Answer 1

Answer:

For the type I error, it's option D

For the type II error, it's option B

Step-by-step explanation:

A) A type I error is when we reject the null hypothesis even if it is true.

Let's set up the two hypotheses;

Null Hypothesis:

H0: p = 0.15

It represents: "The proportion of people who write with their left hand is equal to 0.15."

Alternative Hypothesis:

H1: p ≠ 0.15

In English: "The proportion of people who write with their left hand is different from 0.15" i.e not equal to 0.15

If we make a type I error, then it means we reject H0 (the null hypothesis) and go with the alternative hypothesis (H1). However, the reality is that H0 was the true hypothesis all along.

Thus, we reject the claim that the The proportion of people who write with their left hand is equal to 0.15 when in reality the proportion is actually 0.15

This means the answer for the first part is Option D

B) A type II error is when we fail to reject the null and must "accept" the null; however, the reality is that the alternative hypothesis was the true hypothesis. Hence, making a type two error means we reject the second hypothesis and make a mistake in doing so.

If we make a type II error, then we fail to reject the claim that proportion of people who write with their left hand is equal to 0.15, when the proportion is actually different from 0.15

Thus, he answer is Option B