Question

What is the Type I error in the context of this hypothesis test for the claim that the proportion of left-handed women is less than 10%?

Option 1: Rejecting the claim when it is true.
Option 2: Accepting the claim when it is false.
Option 3: Failing to reject the claim when it is true.
Option 4: None of the above.

Answer 1

In a hypothesis test, a Type I error occurs when we wrongly reject a true null hypothesis, which in this case means rejecting the claim that the proportion of left-handed women is less than 10% when it actually is.

Step-by-step explanation:

In the context of a hypothesis test for the claim that the proportion of left-handed women is less than 10%:

Type I error is made when we reject a true null hypothesis. In this specific case, it would mean that we incorrectly reject the claim that the proportion of left-handed women is less than 10%, even when it actually is less than 10%. Therefore, Option 1: Rejecting the claim when it is true, represents a Type I error.

It is important to note that both Type I and Type II errors are related to the concept of proportion in this hypothesis test, which involves determining whether statistical evidence supports a specific claim about a population proportion.