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 0.18 . 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 0.18 when the proportion is actually 0.18 . B. Reject the claim that the proportion of people who write with their left hand is 0.18 when the proportion is actually different from 0.18 . C. Reject the claim that the proportion of people who write with their left hand is 0.18 when the proportion is actually 0.18 . D. Fail to reject the claim that the proportion of people who write with their left hand is 0.18 when the proportion is actually different from 0.18 . Which of the following is a type II error? A. Reject the claim that the proportion of people who write with their left hand is 0.18 when the proportion is actually different from 0.18 . B. Fail to reject the claim that the proportion of people who write with their left hand is 0.18 when the proportion is actually 0.18 . C. Fail to reject the claim that the proportion of people who write with their left hand is 0.18 when the proportion is actually different from 0.18 . D. Reject the claim that the proportion of people who write with their left hand is 0.18 when the proportion is actually 0.18 .
Solution
Step 1 ：This question is about understanding the concepts of Type I and Type II errors in hypothesis testing.
Step 2 ：A Type I error occurs when we reject the null hypothesis when it is actually true. In this case, the null hypothesis is that the proportion of people who write with their left hand is 0.18. So, a Type I error would be to reject this claim when the proportion is actually 0.18.
Step 3 ：A Type II error occurs when we fail to reject the null hypothesis when it is actually false. In this case, a Type II error would be to fail to reject the claim that the proportion of people who write with their left hand is 0.18 when the proportion is actually different from 0.18.
Step 4 ：The Type I error is: \(\boxed{\text{C. Reject the claim that the proportion of people who write with their left hand is 0.18 when the proportion is actually 0.18.}}\)
Step 5 ：The Type II error is: \(\boxed{\text{C. Fail to reject the claim that the proportion of people who write with their left hand is 0.18 when the proportion is actually different from 0.18.}}\)
