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 0.33 . 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 0.33 when the proportion is actually 0.33 . B. Reject the claim that the proportion of people who write with their left hand is 0.33 when the proportion is actually different from 0.33 . C. Reject the claim that the proportion of people who write with their left hand is 0.33 when the proportion is actually 0.33 . D. Fail to reject the claim that the proportion of people who write with their left hand is 0.33 when the proportion is actually different from 0.33 . Get more help . Clear all Check answer
Solution
Step 1 ：In hypothesis testing, a type I error occurs when we reject a true null hypothesis, and a type II error occurs when we fail to reject a false null hypothesis. In this case, the null hypothesis is that the proportion of people who write with their left hand is 0.33.
Step 2 ：A type I error would be rejecting this claim when it is actually true (i.e., the proportion is indeed 0.33), and a type II error would be failing to reject this claim when it is actually false (i.e., the proportion is different from 0.33).
Step 3 ：Therefore, the correct answer to the question 'Which of the following is a type II error?' is: Fail to reject the claim that the proportion of people who write with their left hand is 0.33 when the proportion is actually different from 0.33.
Step 4 ：Final Answer: \(\boxed{D}\)
