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 0.27 . 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 0.27 when the proportion is actually different from 0.27 . B. Reject the claim that the proportion of people who write with their left hand is 0.27 when the proportion is actually 0.27 . c. Fail to reject the claim that the proportion of people who write with their left hand is 0.27 when the proportion is actually different from 0.27 . D. Fail to reject the claim that the proportion of people who write with their left hand is 0.27 when the proportion is actually 0.27 .
Solution
Step 1 ：In hypothesis testing, a type I error occurs when the null hypothesis is true, but is rejected. It is asserting something that is absent, a false hit. A type II error occurs when the null hypothesis is false, but erroneously fails to be rejected. It is failing to assert what is present, a miss.
Step 2 ：In this case, the null hypothesis is that the proportion of people who write with their left hand is 0.27.
Step 3 ：So, a type I error would be to reject this claim when it is actually true (the proportion is indeed 0.27), and a type II error would be to accept this claim when it is actually false (the proportion is not 0.27).
Step 4 ：Therefore, the answer to the first question, 'Which of the following is a type I error?' is option B.
Step 5 ：\(\boxed{\text{B. Reject the claim that the proportion of people who write with their left hand is 0.27 when the proportion is actually 0.27 .}}\)
