Arsenic is toxic to humans and people can be exposed to it through contaminated drinking water, food, dust, and soil. Scientists have devised a non-invasive way to measure a person's level of arsenic poisoning: by examining toenail clippings. In a recent study, scientists measure the level of arsenic (in mg/kg) in toenail clippings of 8 people who lived near a former arsenic mine in Great Britain. The following levels are recorded. 0.8, 1.9, 2.7, 3.4, 3.9, 7.1, 11.9, 26.0 Below are the summary statistics of the data. min Q1 median Q3 max sd n mean 0.8 2.5 3.65 8.3 26 7.2125 8.368041 8 Suppose the 8 people examined were randomly sampled from residents near the former arsenic mine. Is it legitimate to construct a 95% confidence interval for the mean level of arsenic (in mg/kg) in toenail clippings for residents near the former arsenic mine using a t-distribution? Explain briefly.
Arsenic is toxic to humans and people can be exposed to it through contaminated drinking water, food, dust, and soil. Scientists have devised a non-invasive way to measure a person's level of arsenic poisoning: by examining toenail clippings. In a recent study, scientists measure the level of arsenic (in mg/kg) in toenail clippings of 8 people who lived near a former arsenic mine in Great Britain. The following levels are recorded. 0.8, 1.9, 2.7, 3.4, 3.9, 7.1, 11.9, 26.0 Below are the summary statistics of the data. min Q1 median Q3 max sd n mean 0.8 2.5 3.65 8.3 26 7.2125 8.368041 8 Suppose the 8 people examined were randomly sampled from residents near the former arsenic mine. Is it legitimate to construct a 95% confidence interval for the mean level of arsenic (in mg/kg) in toenail clippings for residents near the former arsenic mine using a t-distribution? Explain briefly.
MATLAB: An Introduction with Applications
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![### Arsenic Exposure in Humans
Arsenic is toxic to humans, and people can be exposed to it through contaminated drinking water, food, dust, and soil. Scientists have devised a non-invasive way to measure a person’s level of arsenic poisoning by examining toenail clippings. In a recent study, scientists measured the level of arsenic (in mg/kg) in the toenail clippings of 8 people who lived near a former arsenic mine in Great Britain. The following levels are recorded:
0.8, 1.9, 2.7, 3.4, 3.9, 7.1, 11.9, 26.0
Below are the summary statistics of the data:
| min | Q1 | median | Q3 | max | mean | sd | n |
|-----|------|--------|-----|-----|------|----------|----|
| 0.8 | 2.5 | 3.65 | 8.3 | 26 | 7.2125 | 8.368041 | 8 |
### Statistical Analysis
Suppose the 8 people examined were randomly sampled from residents near the former arsenic mine. Is it legitimate to construct a 95% confidence interval for the mean level of arsenic (in mg/kg) in toenail clippings for residents near the former arsenic mine using a t-distribution? Explain briefly.
### Explanation
- **Random Sampling**: The data collection method assumes that the 8 people were randomly sampled. Random sampling is essential for ensuring that the sample is representative of the broader population living near the arsenic mine.
- **Sample Size**: Given that the sample size (n=8) is small, the t-distribution is appropriate for constructing confidence intervals. The t-distribution is particularly useful for small sample sizes and when the population standard deviation is unknown.
- **Confidence Interval Using t-Distribution**: With the provided mean (7.2125 mg/kg) and standard deviation (8.368041 mg/kg), one can use the t-distribution to construct a 95% confidence interval. The general formula for the confidence interval is given by:
\[\text{CI} = \bar{x} \pm t_{\alpha/2, \; df} \times \left(\frac{s}{\sqrt{n}}\right)\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1207d66c-1291-4aaf-89f2-2ae1ecfc9f88%2F1fe9e942-ded7-432c-9a44-ada2ce79549b%2Fb82b7nq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Arsenic Exposure in Humans
Arsenic is toxic to humans, and people can be exposed to it through contaminated drinking water, food, dust, and soil. Scientists have devised a non-invasive way to measure a person’s level of arsenic poisoning by examining toenail clippings. In a recent study, scientists measured the level of arsenic (in mg/kg) in the toenail clippings of 8 people who lived near a former arsenic mine in Great Britain. The following levels are recorded:
0.8, 1.9, 2.7, 3.4, 3.9, 7.1, 11.9, 26.0
Below are the summary statistics of the data:
| min | Q1 | median | Q3 | max | mean | sd | n |
|-----|------|--------|-----|-----|------|----------|----|
| 0.8 | 2.5 | 3.65 | 8.3 | 26 | 7.2125 | 8.368041 | 8 |
### Statistical Analysis
Suppose the 8 people examined were randomly sampled from residents near the former arsenic mine. Is it legitimate to construct a 95% confidence interval for the mean level of arsenic (in mg/kg) in toenail clippings for residents near the former arsenic mine using a t-distribution? Explain briefly.
### Explanation
- **Random Sampling**: The data collection method assumes that the 8 people were randomly sampled. Random sampling is essential for ensuring that the sample is representative of the broader population living near the arsenic mine.
- **Sample Size**: Given that the sample size (n=8) is small, the t-distribution is appropriate for constructing confidence intervals. The t-distribution is particularly useful for small sample sizes and when the population standard deviation is unknown.
- **Confidence Interval Using t-Distribution**: With the provided mean (7.2125 mg/kg) and standard deviation (8.368041 mg/kg), one can use the t-distribution to construct a 95% confidence interval. The general formula for the confidence interval is given by:
\[\text{CI} = \bar{x} \pm t_{\alpha/2, \; df} \times \left(\frac{s}{\sqrt{n}}\right)\]
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