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 0.22.

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 0.29 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 different from 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 0.29
D. 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

Answer 1

Type I error is 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.

Type II error is Fail to reject the claim that the proportion of people who write with their left hand is 0.29 when the proportion is different from 0.29.

Explanation:

We are given the following hypothesis below;

Let p = proportion of people who write with their left hand

So, Null Hypothesis,
`H_0` : p = 0.22 {means that the proportion of people who write with their left hand is equal to 0.22}

Alternate Hypothesis,
`H_A` : p
`\\eq` 0.22 {means that the proportion of people who write with their left hand is different from 0.22}

Now, Type I error states that we conclude that the null hypothesis is rejected when in fact the null hypothesis was actually true. Or in other words, it is the probability of rejecting a true hypothesis.

So, in our question; Type I error is 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.

Type II error states that we conclude that the null hypothesis is accepted when in fact the null hypothesis was actually false. Or in other words, it is the probability of accepting a false hypothesis.

So, in our question; Type II error is Fail to reject the claim that the proportion of people who write with their left hand is 0.29 when the proportion is different from 0.29.