Mothers under 20 years old. Previous sociologists claimed that only 5% of all births in the United States were to mothers under 20 years of age. The sociologist conducts a simple random sample of 100 births of infants who were mothers under 20 years of age. Test the sociologist's claim and find that the 0.06 level of significance is not met.
Question: How many percent of all mothers are under 20 years of age in the United States?
Answer: 10%
Since np(1 - p) >= 10, we should use the normal distribution to obtain the Z-value.
What are the null and alternative hypotheses?
H0: p = 0.05 (The proportion of mothers under 20 years of age is 5%)
Ha: p ≠ 0.05 (The proportion of mothers under 20 years of age is not 5%)
Based on the hypotheses, calculate the p-value using the Z-scores.
Method: Markout being given that the population is normally distributed and that np >= 10 and n(1 - p) >= 10 for the binomial distribution, we can assume that the sample proportion follows a normal distribution.