Question

Determine the null and alternative hypotheses, (b) explain what it would mean to make a type I error, and (c) explain what it would mean to make a type II error.Six years ago, 11.7% of registered births were to teenage mothers. A sociologist believes that the percentage has decreased since then.Question content area bottomPart 1(a) Which of the following is the hypothesis test to be conducted?A.H0: p=0.117, H1: p>0.117B.H0: p=0.117, H1: p≠0.117C.H0: p=0.117, H1: p<0.117Part 2(b) Which of the following is a type I error?A.The sociologist rejects the hypothesis that the percentage of births to teenage mothers is 11.7%, when it is the true percentage.B.The sociologist fails to reject the hypothesis that the percentage of births to teenage mothers is 11.7%, when the true percentage is less than 11.7%.C.The sociologist rejects the hypothesis that the percentage of births to teenage mothers is 11.7%, when the true percentage is less than 11.7%.Part 3(c) Which of the following is a type II error?A.The sociologist fails to reject the hypothesis that the percentage of births to teenage mothers is 11.7%, when it is the true percentage.b) Which of the following is a type I error?A.The sociologist rejects the hypothesis that the percentage of births to teenage mothers is 11.7%, when it is the true percentage.B.The sociologist fails to reject the hypothesis that the percentage of births to teenage mothers is 11.7%, when the true percentage is less than 11.7%.C.The sociologist rejects the hypothesis that the percentage of births to teenage mothers is 11.7%, when the true percentage is less than 11.7%.Part 3(c) Which of the following is a type II error?A.The sociologist fails to reject the hypothesis that the percentage of births to teenage mothers is 11.7%, when it is the true percentage.B.The sociologist rejects the hypothesis that the percentage of births to teenage mothers is 11.7%, when it is the true percentage.C.The sociologist fails to reject the hypothesis that the percentage of births to teenage mothers is 11.7%, when the true percentage is less than

Answer 1

- To solve the question, we simply need to know the definitions of Type I and Type II errors in Hypothesis Testing.

Type I error:

A type I error occurs during hypothesis testing when a null hypothesis is rejected, even though it is accurate and should not be rejected.

Type II error:

This is an error that describes the error that occurs when one fails to reject a null hypothesis that is actually false.

- Applying these definitions above, we have:

Question B:

- The only one that follows the definition of a Type I error is,

"The sociologist rejects the hypothesis that the percentage of births to teenage mothers is 11.7​%, when it is the true percentage."

- Thus, the answer is OPTION A

Question C:

- The only option that follows the definition of a Type II error is,

"The sociologist fails to reject the hypothesis that the percentage of births to teenage mothers is 11.7​%, when the true percentage is less than"

- Thus, the answer is OPTION C