MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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### Estimating Average Blood Alcohol Concentration (BAC) in Fatal Accidents

A researcher aims to estimate the average blood alcohol concentration (BAC) for drivers involved in fatal accidents who are confirmed to have positive BAC values. Data from 51 such drivers in 2009 indicates the sample mean BAC to be 0.16 g/dL with a standard deviation of 0.080 g/dL. The following sections address specific requirements and interpretations based on this data.

#### Part (a)
The necessity for a large sample size arises due to the skewed distribution of blood alcohol concentrations:
- **Correct Answer:** D. Since the distribution of blood alcohol concentrations is highly skewed right, a large sample size is needed to minimize the margin of error to ensure only the peak of the sampling distribution is captured in the confidence interval.

#### Part (b)
There were approximately 25,000 fatal crashes involving drivers with a positive BAC. The data was obtained using a simple random sample. To satisfy requirements for constructing a confidence interval:
- **Correct Answer:** C. The sample size is likely less than 5% of the population.

#### Part (c)
Determine and interpret a 90% confidence interval for the mean BAC in fatal crashes with a positive BAC. Choose and complete the correct option:
- **Choose Ascending Order. Round to three decimal places as needed.**
  
  **Options:**
  - **A:** There is a \( \square \)% probability that the population mean BAC is between \( \square \) and \( \square \) for drivers involved in fatal accidents who have a positive BAC value.
  - **B:** The researcher is \( \square \)% confident that the population mean BAC is between \( \square \) and \( \square \) for drivers involved in fatal accidents who have a positive BAC value.
  - **C:** The researcher is \( \square \)% confident that the population mean BAC is not between \( \square \) and \( \square \) for drivers involved in fatal accidents who have a positive BAC value.

This text aims to clarify how to approach statistical analysis in real-world contexts and ensure accurate interpretation based on sample data and established methodologies.
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Transcribed Image Text:### Estimating Average Blood Alcohol Concentration (BAC) in Fatal Accidents A researcher aims to estimate the average blood alcohol concentration (BAC) for drivers involved in fatal accidents who are confirmed to have positive BAC values. Data from 51 such drivers in 2009 indicates the sample mean BAC to be 0.16 g/dL with a standard deviation of 0.080 g/dL. The following sections address specific requirements and interpretations based on this data. #### Part (a) The necessity for a large sample size arises due to the skewed distribution of blood alcohol concentrations: - **Correct Answer:** D. Since the distribution of blood alcohol concentrations is highly skewed right, a large sample size is needed to minimize the margin of error to ensure only the peak of the sampling distribution is captured in the confidence interval. #### Part (b) There were approximately 25,000 fatal crashes involving drivers with a positive BAC. The data was obtained using a simple random sample. To satisfy requirements for constructing a confidence interval: - **Correct Answer:** C. The sample size is likely less than 5% of the population. #### Part (c) Determine and interpret a 90% confidence interval for the mean BAC in fatal crashes with a positive BAC. Choose and complete the correct option: - **Choose Ascending Order. Round to three decimal places as needed.** **Options:** - **A:** There is a \( \square \)% probability that the population mean BAC is between \( \square \) and \( \square \) for drivers involved in fatal accidents who have a positive BAC value. - **B:** The researcher is \( \square \)% confident that the population mean BAC is between \( \square \) and \( \square \) for drivers involved in fatal accidents who have a positive BAC value. - **C:** The researcher is \( \square \)% confident that the population mean BAC is not between \( \square \) and \( \square \) for drivers involved in fatal accidents who have a positive BAC value. This text aims to clarify how to approach statistical analysis in real-world contexts and ensure accurate interpretation based on sample data and established methodologies.
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