Six Years ago, 12.2% of registered births were to teenage mothers. A sociologist believes that the percentage has decreased since then.
(a) Which of the following is the hypothesis to be conducted?
A. H0: p = 0.122, H1 p > 0.122
B. H0: p = 0.122, H1 p <> 0.122
C. H0: p = 0.122, H1 p < 0.122
(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 12.2%, when the true percentage is less than 12.2%
B. The sociologist fails to reject the hypothesis that the percentage of births to teenage mothers is 12.2%, when the true percentage is less than 12.2%
C. The sociologist rejects the hypothesis that the percentage of births to teenage mothers is 12.2%, when it is the true percentage.
c) Which of the following is a Type II error?
A. The sociologist rejects the hypothesis that the percentage of births to teenage mothers is 12.2%, when it is the true percentage
B. The sociologist fails to reject the hypothesis that the percentage of births to teenage mothers is 12.2%, when it is the true percentage
C. The sociologist fails to reject the hypothesis that the percentage of births to teenage mothers is 12.2%, when the true percentage is less than 12.2%
(a) C H0: p = 0.122, H1: p < 0.122
because a null hypothesis should take the opposite of what is being assumed. So the assumption is that nothing has changed while the hypothesis is that the rate has decreased.
(b) C. The sociologist rejects the hypothesis that the percentage of births to teenage mothers is 12.2%, when it is the true percentage. Type I Error is rejecting the null hypothesis when it is true
c) C. The sociologist fails to reject the hypothesis that the percentage of births to teenage mothers is 12.2%, when the true percentage is less than 12.2% Type II Error is accepting the null hypothesis when it is false.
(a) Which of the following is the hypothesis to be conducted?
A. H0: p = 0.122, H1 p > 0.122
B. H0: p = 0.122, H1 p <> 0.122
C. H0: p = 0.122, H1 p < 0.122
(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 12.2%, when the true percentage is less than 12.2%
B. The sociologist fails to reject the hypothesis that the percentage of births to teenage mothers is 12.2%, when the true percentage is less than 12.2%
C. The sociologist rejects the hypothesis that the percentage of births to teenage mothers is 12.2%, when it is the true percentage.
c) Which of the following is a Type II error?
A. The sociologist rejects the hypothesis that the percentage of births to teenage mothers is 12.2%, when it is the true percentage
B. The sociologist fails to reject the hypothesis that the percentage of births to teenage mothers is 12.2%, when it is the true percentage
C. The sociologist fails to reject the hypothesis that the percentage of births to teenage mothers is 12.2%, when the true percentage is less than 12.2%
(a) C H0: p = 0.122, H1: p < 0.122
because a null hypothesis should take the opposite of what is being assumed. So the assumption is that nothing has changed while the hypothesis is that the rate has decreased.
(b) C. The sociologist rejects the hypothesis that the percentage of births to teenage mothers is 12.2%, when it is the true percentage. Type I Error is rejecting the null hypothesis when it is true
c) C. The sociologist fails to reject the hypothesis that the percentage of births to teenage mothers is 12.2%, when the true percentage is less than 12.2% Type II Error is accepting the null hypothesis when it is false.