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=0.1level of significance.

Preliminary:

1. Is it safe to assume thatn5% of all mothers under 20 years of age in the United States?

• Yes
• No

3.Verifynp(1p)10Round your answer to one decimal place.

np(1-p)=

4.Sincenp(1-p)<10

, we should use which distribution to obtain thep-value?

• binomial distribution
• exponential distribution
• uniform distribution

Note:Without being given that the population is normally distributed, and thatnp(1-p)<10

, we cannot assume normal distribution and are required to use the binomial distribution.

Test the claim:

1. What are the null and alternative hypotheses?
2. H0:?

p

=<>

H1:?

p

<>=

1. Based on the hypotheses, calculate thep-value using the binomial distribution.Round to four decimal places.
2. p-value =
3. Make a decision.

Fail to reject the null hypothesis.

Reject the null hypothesis.

4.Make a conclusion regarding the claim.

There is not enough evidence to support the claim

There is enough evidence to support the claim

that the population of births to mothers under 20 years of age in the United States is decreasing.