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 0.21. 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 0.21 when the proportion is actually different from 0.21. b. fail to reject the claim that the proportion of people who write with their left hand is 0.21 when the proportion is actually 0.21. c. reject the claim that the proportion of people who write with their left hand is 0.21 when the proportion is actually 0.21. d. fail to reject the claim that the proportion of people who write with their left hand is 0.21 when the proportion is actually different from 0.21.

Explanation:

A Type I error occurs when we reject a null hypothesis that is actually true. In this case, the null hypothesis is that the proportion of people who write with their left - hand is 0.21.

• Option A: Rejecting the claim when the proportion is actually different (so the null is false) is not a Type I error.
• Option B: Failing to reject when the null is true is a correct decision, not an error.
• Option C: Rejecting the claim (null hypothesis) when the proportion (null hypothesis) is actually 0.21 (true) is a Type I error.
• Option D: Failing to reject when the null is false is a Type II error.

Answer:

C. Reject the claim that the proportion of people who write with their left hand is 0.21 when the proportion is actually 0.21.