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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.

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section: Chapter Questions
Problem 8CR
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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.
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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