Question

In 2006, 12.7% 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. The sociologist conducts a simple random sample of 44 births and finds that 5 of them were to mothers under 20 years of age. Test the sociologist's claim at the $\alpha = 0.01$ level of significance. Preliminary: a. Is it safe to assume that $n < 5\%$ of all mothers under 20 years of age in the United States? • Yes ? No b. Verify $np(1 - p) > 10$. Round your answer to one decimal place. $np(1 - p) = 4.9$ c. Since $np(1 - p) < 10$, we should use which distribution to obtain the $p$-value? • exponential distribution ? binomial distribution • uniform distribution Note: Without being given that the population is normally distributed, and that $np(1 - p) < 10$, we cannot assume normal distribution and are required to use the binomial distribution. Test the claim: a. What are the null and alternative hypotheses? $H_0: p$ $H_1: p$ 0.127 b. Based on the hypotheses, calculate the $p$-value using the binomial distribution. Round to four decimal places. p-value = Hint: Did you use the binomial distribution, i.e., binomcdf(n,p,x)? c. Make a decision. ? Fail to reject the null hypothesis. d. Make a conclusion regarding the claim. ? There is not enough evidence to support the claim that the population of births to mothers under 20 years of age in the United States is decreasing.

          In 2006, 12.7% 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. The sociologist conducts a simple random
sample of 44 births and finds that 5 of them were to mothers under 20 years of age. Test the sociologist's
claim at the $\alpha = 0.01$ level of significance.
Preliminary:
a. Is it safe to assume that $n < 5\%$ of all mothers under 20 years of age in the United States?
• Yes
? No
b. Verify $np(1 - p) > 10$. Round your answer to one decimal place.
$np(1 - p) = 4.9$
c. Since $np(1 - p) < 10$, we should use which distribution to obtain the $p$-value?
• exponential distribution
? binomial distribution
• uniform distribution
Note: Without being given that the population is normally distributed, and that $np(1 - p) < 10$, we cannot
assume normal distribution and are required to use the binomial distribution.
Test the claim:
a. What are the null and alternative hypotheses?
$H_0: p$
$H_1: p$
0.127
b. Based on the hypotheses, calculate the $p$-value using the binomial distribution. Round to four decimal
places.
p-value =
Hint: Did you use the binomial distribution, i.e., binomcdf(n,p,x)?
c. Make a decision.
? Fail to reject the null hypothesis.
d. Make a conclusion regarding the claim.
? There is not enough evidence to support the claim that the population of births to mothers under 20
years of age in the United States is decreasing.

In 2006, 12.7% 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. The sociologist conducts a simple random
sample of 44 births and finds that 5 of them were to mothers under 20 years of age. Test the sociologist's
claim at the α = 0.01 level of significance.
Preliminary:
a. Is it safe to assume that n < 5% of all mothers under 20 years of age in the United States?
• Yes
? No
b. Verify np(1 - p) > 10. Round your answer to one decimal place.
np(1 - p) = 4.9
c. Since np(1 - p) < 10, we should use which distribution to obtain the p-value?
• exponential distribution
? binomial distribution
• uniform distribution
Note: Without being given that the population is normally distributed, and that np(1 - p) < 10, we cannot
assume normal distribution and are required to use the binomial distribution.
Test the claim:
a. What are the null and alternative hypotheses?
H0: p
H1: p
0.127
b. Based on the hypotheses, calculate the p-value using the binomial distribution. Round to four decimal
places.
p-value =
Hint: Did you use the binomial distribution, i.e., binomcdf(n,p,x)?
c. Make a decision.
? Fail to reject the null hypothesis.
d. Make a conclusion regarding the claim.
? There is not enough evidence to support the claim that the population of births to mothers under 20
years of age in the United States is decreasing.

Added by Beatriz J.

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