In 2006, 25.7% 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. She conducts a simple random sample of 70 births and finds that 16 of them were to mothers under 20 years of age. Test the sociologist’s claim at the α = 0.2 level of significance. (a) Formulate the null and alternative hypotheses.
Question
In 2006, 25.7% 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. She conducts a simple random sample of 70 births and finds that 16 of them were to mothers under 20 years of age. Test the sociologist’s claim at the α = 0.2 level of significance. (a) Formulate the null and alternative hypotheses.
Solution
The null hypothesis (H0) and the alternative hypothesis (H1) are the two basic hypotheses in any statistical test.
(a) The null hypothesis (H0): The proportion of births to mothers under 20 years of age is 25.7% (or 0.257). This hypothesis assumes that the sociologist's claim is not true and that the proportion has not decreased.
The alternative hypothesis (H1): The proportion of births to mothers under 20 years of age is less than 25.7% (or 0.257). This hypothesis supports the sociologist's claim that the proportion has decreased.
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