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(c) What is the probability of not concluding that more than 20% of the population is obese when the actual percentage of obese individuals is 2416? (Round your answer to four decimal places)

(c) What is the probability of not concluding that more than 20% of the population is obese when the actual percentage of obese individuals is 2416? (Round your answer to four decimal places)

MATLAB: An Introduction with Applications
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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A common characterization of obese individuals is that their body mass index is at least 30 (BMI = weight/(height)^2, where height is in meters and weight is in kilograms). An article reported that in a sample of female workers, 265 had BMIs of less than 25, 156 had BMIs that were at least 25 but less than 30, and 123 had BMI exceeding 30. Is there compelling evidence for concluding that more than 20% of the individuals in the sampled population are obese? ### (a) State the appropriate hypotheses with a significance level of 0.05. - \( H_0: p = 0.20 \) - \( H_a: p > 0.20 \) - \( H_0: p = 0.20 \) - \( H_a: p < 0.20 \) - \( H_0: p = 0.20 \) - \( H_a: p \neq 0.20 \) - \( H_0: p = 0.20 \) - \( H_a: p > 0.20 \) Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) - Test Statistic, \( z = 1.50 \) - P-value = \( 0.0668 \) **Conclusion:** Do not reject the null hypothesis. There is not sufficient evidence that more than 20% of the population of female workers is obese. ### (b) Explain in the context of this scenario what constitutes type I error. - A type I error would be declaring that 20% or less of the population of female workers is obese, when in fact more than 20% are actually obese. **Explain in the context of this scenario what constitutes type II error.** - A type II error would be failing to declare that more than 20% of the population of female workers is obese, when in fact more than 20% are actually obese. ### (c) What is the probability of not concluding that more than 20% of the population is obese when the actual percentage of obese individuals is 24%? (Round your answer to four decimal places.) - \( 0.2033 \)
Transcribed Image Text:A common characterization of obese individuals is that their body mass index is at least 30 (BMI = weight/(height)^2, where height is in meters and weight is in kilograms). An article reported that in a sample of female workers, 265 had BMIs of less than 25, 156 had BMIs that were at least 25 but less than 30, and 123 had BMI exceeding 30. Is there compelling evidence for concluding that more than 20% of the individuals in the sampled population are obese? ### (a) State the appropriate hypotheses with a significance level of 0.05. - \( H_0: p = 0.20 \) - \( H_a: p > 0.20 \) - \( H_0: p = 0.20 \) - \( H_a: p < 0.20 \) - \( H_0: p = 0.20 \) - \( H_a: p \neq 0.20 \) - \( H_0: p = 0.20 \) - \( H_a: p > 0.20 \) Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) - Test Statistic, \( z = 1.50 \) - P-value = \( 0.0668 \) **Conclusion:** Do not reject the null hypothesis. There is not sufficient evidence that more than 20% of the population of female workers is obese. ### (b) Explain in the context of this scenario what constitutes type I error. - A type I error would be declaring that 20% or less of the population of female workers is obese, when in fact more than 20% are actually obese. **Explain in the context of this scenario what constitutes type II error.** - A type II error would be failing to declare that more than 20% of the population of female workers is obese, when in fact more than 20% are actually obese. ### (c) What is the probability of not concluding that more than 20% of the population is obese when the actual percentage of obese individuals is 24%? (Round your answer to four decimal places.) - \( 0.2033 \)
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