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 0.29. 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 0.29 when the proportion is actually different from 0.29. b. fail to reject the claim that the proportion of people who write with their left hand is 0.29 when the proportion is actually 0.29. c. reject the claim that the proportion of people who write with their left hand is 0.29 when the proportion is actually different from 0.29. d. reject the claim that the proportion of people who write with their left hand is 0.29 when the proportion is actually 0.29.

Explanation:

• Type I error: Rejecting a true null hypothesis. In this case, the null hypothesis is that the proportion of people who write with their left - hand is \(p = 0.29\). So, rejecting the claim that \(p=0.29\) when \(p = 0.29\) (as in option D) is a Type I error.
• Type II error: Failing to reject a false null hypothesis. The null hypothesis \(H_0:p = 0.29\). If the actual proportion \(p

eq0.29\) (the null hypothesis is false) and we fail to reject \(H_0\), we make a Type II error.

Answer:

A. Fail to reject the claim that the proportion of people who write with their left hand is \(0.29\) when the proportion is actually different from \(0.29\).