In 2006, 11.5% 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 36 births and finds that 6 of them were to mothers under 20 years of age. Test the sociologist's claim at the a = 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? " No Yes b. Verify np(1 - p) ≥ 10. Round your answer to one decimal place. np(1 - p) 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? Ho: ? H₁: ? p-value = ? ? ◊ b. Based on the hypotheses, calculate the p-value using the binomial distribution. Round to four decimal places. c. Make a decision. Select an answer d. Make a conclusion regarding the claim. Select an answer that the population of births to mothers
In 2006, 11.5% 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 36 births and finds that 6 of them were to mothers under 20 years of age. Test the sociologist's claim at the a = 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? " No Yes b. Verify np(1 - p) ≥ 10. Round your answer to one decimal place. np(1 - p) 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? Ho: ? H₁: ? p-value = ? ? ◊ b. Based on the hypotheses, calculate the p-value using the binomial distribution. Round to four decimal places. c. Make a decision. Select an answer d. Make a conclusion regarding the claim. Select an answer that the population of births to mothers
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![In 2006, 11.5% 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 36 births and finds that 6 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 \( n \leq 5 \% \) of all mothers under 20 years of age in the United States?
- ○ No
- ○ Yes
b. Verify \( np(1-p) \geq 10 \). *Round your answer to one decimal place.*
\[ np(1-p) = \]
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?
\[ H_0: \ \]
\[ H_1: \ \]
b. Based on the hypotheses, calculate the p-value using the binomial distribution. *Round to four decimal places.*
\[ \text{p-value} = \]
c. Make a decision.
- [Select an answer]
d. Make a conclusion regarding the claim.
- [Select an answer] that the population of births to mothers under 20 years of age in the United States is decreasing.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F078de29d-732f-4e63-accc-2adc1016c930%2Fcf22bce6-293e-45f1-a7c5-413c0a4a87d9%2F4xlhfcl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In 2006, 11.5% 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 36 births and finds that 6 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 \( n \leq 5 \% \) of all mothers under 20 years of age in the United States?
- ○ No
- ○ Yes
b. Verify \( np(1-p) \geq 10 \). *Round your answer to one decimal place.*
\[ np(1-p) = \]
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?
\[ H_0: \ \]
\[ H_1: \ \]
b. Based on the hypotheses, calculate the p-value using the binomial distribution. *Round to four decimal places.*
\[ \text{p-value} = \]
c. Make a decision.
- [Select an answer]
d. Make a conclusion regarding the claim.
- [Select an answer] that the population of births to mothers under 20 years of age in the United States is decreasing.
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