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, 159 had BMIS that were at least 25 but less than 30, and 121 had BMIS exceeding 30. Is there compelling evidence for concluding that more than 20% of the individuals in the sampled population are obese? LAUSE SALT (a) State the appropriate hypothe Open SALT in a new tab e level of 0.05. Ho: P = 0.20 H: P<0.20 Ho: P = 0.20 H₂: p > 0.20 Ho: p > 0.20 H₂: P = 0.20 Ho: P = 0.20 H₂: 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.) Z= P-value = What can you conclude? O Do not reject the null hypothesis. There is not sufficient evidence that more than 20% of the population of female workers is obese. O Do not reject the null hypothesis. There is sufficient evidence that more than 20% of the population of female workers is obese. O Reject the null hypothesis. There is sufficient evidence that more than 20% of the population of female workers is obese. O 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. A type I error would be declaring that 20% or more of the population of female workers is obese, when in fact less than 20% are actually obese. A type I error would he declaring that lore than 3000
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, 159 had BMIS that were at least 25 but less than 30, and 121 had BMIS exceeding 30. Is there compelling evidence for concluding that more than 20% of the individuals in the sampled population are obese? LAUSE SALT (a) State the appropriate hypothe Open SALT in a new tab e level of 0.05. Ho: P = 0.20 H: P<0.20 Ho: P = 0.20 H₂: p > 0.20 Ho: p > 0.20 H₂: P = 0.20 Ho: P = 0.20 H₂: 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.) Z= P-value = What can you conclude? O Do not reject the null hypothesis. There is not sufficient evidence that more than 20% of the population of female workers is obese. O Do not reject the null hypothesis. There is sufficient evidence that more than 20% of the population of female workers is obese. O Reject the null hypothesis. There is sufficient evidence that more than 20% of the population of female workers is obese. O 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. A type I error would be declaring that 20% or more of the population of female workers is obese, when in fact less than 20% are actually obese. A type I error would he declaring that lore than 3000
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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Question
![**Educational Resource: Hypothesis Testing for Obesity in a Population**
A common characterization of obese individuals is that their body mass index (BMI) is at least 30 \([BMI = \text{weight}/(\text{height})^2]\), 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, 159 had BMIs that were at least 25 but less than 30, and 121 had BMIs exceeding 30. We examine if there is compelling evidence for concluding that more than 20% of the individuals in the sampled population are obese.
### Hypothesis Testing
**(a) State the appropriate hypothesis and level of significance:** 0.05
- \(H_0\): \(p = 0.20\)
- \(H_a\): \(p > 0.20\)
**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 \(z =\) [blank]
- P-value = [blank]
**Conclusion Options**:
1. Do not reject the null hypothesis. There is not sufficient evidence that more than 20% of the population of female workers is obese.
2. Do not reject the null hypothesis. There is sufficient evidence that more than 20% of the population of female workers is obese.
3. Reject the null hypothesis. There is sufficient evidence that more than 20% of the population of female workers is obese.
4. Reject the null hypothesis. There is not sufficient evidence that more than 20% of the population of female workers is obese.
**(b) Explain a type I error in this context:**
- 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.
- A type I error would be declaring that more than 20% of the population of female workers is obese, when in fact 20% or less are actually obese.
- A type I error would be declaring that less than 20% of the population of female workers is obese, when it is not true.
**Graph or Diagram Explanation:**
There is no graph or diagram included in this content. The focus is on determining statistical conclusions based on the given data and hypothesis](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F379782e3-36e2-4b06-9a33-e2601af30423%2Ff0cadc02-359b-4bab-b77e-8205e941590a%2Fi2sd94h_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Resource: Hypothesis Testing for Obesity in a Population**
A common characterization of obese individuals is that their body mass index (BMI) is at least 30 \([BMI = \text{weight}/(\text{height})^2]\), 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, 159 had BMIs that were at least 25 but less than 30, and 121 had BMIs exceeding 30. We examine if there is compelling evidence for concluding that more than 20% of the individuals in the sampled population are obese.
### Hypothesis Testing
**(a) State the appropriate hypothesis and level of significance:** 0.05
- \(H_0\): \(p = 0.20\)
- \(H_a\): \(p > 0.20\)
**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 \(z =\) [blank]
- P-value = [blank]
**Conclusion Options**:
1. Do not reject the null hypothesis. There is not sufficient evidence that more than 20% of the population of female workers is obese.
2. Do not reject the null hypothesis. There is sufficient evidence that more than 20% of the population of female workers is obese.
3. Reject the null hypothesis. There is sufficient evidence that more than 20% of the population of female workers is obese.
4. Reject the null hypothesis. There is not sufficient evidence that more than 20% of the population of female workers is obese.
**(b) Explain a type I error in this context:**
- 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.
- A type I error would be declaring that more than 20% of the population of female workers is obese, when in fact 20% or less are actually obese.
- A type I error would be declaring that less than 20% of the population of female workers is obese, when it is not true.
**Graph or Diagram Explanation:**
There is no graph or diagram included in this content. The focus is on determining statistical conclusions based on the given data and hypothesis
Expert Solution
Step 1: State the problem
It is required to determine whether there is compelling evidence to conclude that more than 20% of individuals in the population are obese.
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