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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 a = 0.1 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? O exponential distribution uniform distribution O 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 ? ? ◇ b. Based on the hypotheses, calculate the p-value using the binomial distribution. Round to four decimal places. 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.

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 a = 0.1 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? O exponential distribution uniform distribution O 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 ? ? ◇ b. Based on the hypotheses, calculate the p-value using the binomial distribution. Round to four decimal places. 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.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 4BGP
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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 a = 0.1 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? O exponential distribution uniform distribution O 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 ? ? ◇ b. Based on the hypotheses, calculate the p-value using the binomial distribution. Round to four decimal places. 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.
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 a = 0.1 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? O exponential distribution uniform distribution O 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 ? ? ◇ b. Based on the hypotheses, calculate the p-value using the binomial distribution. Round to four decimal places. 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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