In 2006, 12.5% 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 6 of them were to mothers under 20 years of age. Test the sociologist's claim at the 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? No Yes b. Verify np(1 - p) ≥ 10. Round your answer to one decimal place. np(1 - p) = 5.0 c. Since np(1 - p) < 10, we should use which distribution to obtain the p-value? exponential distribution uniform distribution binomial 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? Hop H1: p 0.125 0.125 b. Based on the hypotheses, calculate the p-value using the binomial distribution. Round to four decimal places. -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, 12.5% 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 6 of them were to mothers under 20 years of age. Test the sociologist's claim at the 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? No Yes b. Verify np(1 - p) ≥ 10. Round your answer to one decimal place. np(1 - p) = 5.0 c. Since np(1 - p) < 10, we should use which distribution to obtain the p-value? exponential distribution uniform distribution binomial 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? Hop H1: p 0.125 0.125 b. Based on the hypotheses, calculate the p-value using the binomial distribution. Round to four decimal places. -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.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section: Chapter Questions
Problem 8SGR
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Transcribed Image Text:In 2006, 12.5% 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 6 of them were to mothers under 20 years of
age. Test the sociologist's claim at the
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?
No
Yes
b. Verify np(1 - p) ≥ 10. Round your answer to one
decimal place.
np(1 - p) = 5.0
c. Since np(1 - p) < 10, we should use which
distribution to obtain the p-value?
exponential distribution
uniform distribution
binomial 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?
Hop
H1: p
0.125
0.125
b. Based on the hypotheses, calculate the p-value using
the binomial distribution. Round to four decimal
places.
-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.
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