In 2006, 10.6% of all live births in the United States were to mothers under 20 years of age.

Question

In 2006, 10.6% of all live births in the United States were to mothers under 20 years of age. A sociologist claims that births to mothers under 20 years of age is decreasing. The sociologist conducts a simple random sample of 46 births and finds that 4 of them were to mothers under 20 years of age. Test the sociologist's claim at the a=0.05 level of significance. Based on the hypotheses, calculate the p-value using the binomial distribution. Verify np(1-p)>10. np(1-p).

Answer 1

10.6

4/46 = 2/23 = 0.087 = 8.7% which is close to but a little less than 10.6%

Ho: mu=10.6

H1: mu<10.6

1 tailed test, n=46 use T test, df= 45

use t tables to find t critical

if t calc > t crit, reject Ho