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 I error? A. 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 . B. 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 . 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 0.33 .
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The Deep Dive
If you're looking to distinguish between Type I and Type II errors, think of it like this: a Type I error happens when you sound the alarm when there's no fire! So in your case, the correct answer is A. You'd mistakenly reject the claim that the proportion of left-handed people is 0.33, even when it truly is different. Now, on the flip side, a Type II error is like failing to notice the fire when it actually exists! In this scenario, that would be option B, where you fail to reject the claim that the proportion is 0.33, while it’s actually different. It's always a balancing act in hypothesis testing!
