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In a random sample of six people, the mean driving distance to work was 18.8 miles and the standard deviation was 4.5 miles. Assume the population is normally distributed and use the t-distribution to find the margin of error and construct a 90% confidence interval for the population mean μ. Interpret the results. Identify the margin of error. ▼ (Round to one decimal place as needed.). Construct a 90% confidence interval for the population mean. (Round to one decimal place as needed.) Interpret the results. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) O A. % of all random samples of six people from the population will have a mean driving distance to work (in miles) that is between the interval's endpoints. OB. With % confidence, it can be said that most driving distances to work (in miles) in the population are between the interval's endpoints. OC. With % confidence, it can be said that the population mean driving distance to work (in miles) is between the interval's endpoints. OD. It can be said that % of the population has a driving distance to work (in miles) that is between the interval's endpoints.

In a random sample of six people, the mean driving distance to work was 18.8 miles and the standard deviation was 4.5 miles. Assume the population is normally distributed and use the t-distribution to find the margin of error and construct a 90% confidence interval for the population mean μ. Interpret the results. Identify the margin of error. ▼ (Round to one decimal place as needed.). Construct a 90% confidence interval for the population mean. (Round to one decimal place as needed.) Interpret the results. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) O A. % of all random samples of six people from the population will have a mean driving distance to work (in miles) that is between the interval's endpoints. OB. With % confidence, it can be said that most driving distances to work (in miles) in the population are between the interval's endpoints. OC. With % confidence, it can be said that the population mean driving distance to work (in miles) is between the interval's endpoints. OD. It can be said that % of the population has a driving distance to work (in miles) that is between the interval's endpoints.

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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### Driving Distance Confidence Interval Calculation In a random sample of six people, the mean driving distance to work was 18.8 miles and the standard deviation was 4.5 miles. Assume the population is normally distributed and use the t-distribution to find the margin of error and construct a 90% confidence interval for the population mean \( \mu \). Interpret the results. #### Steps for Calculation: 1. **Identify the Margin of Error:** - Use the dropdown menu to select the appropriate margin of error (MoE). - Round the margin of error to one decimal place as needed. **Margin of Error:** \[ \boxed{} \] (Round to one decimal place as needed.) 2. **Construct a 90% Confidence Interval for the Population Mean:** - Compute the confidence interval using the sample mean and the margin of error. - The interval will be in the form \( ( \text{lower bound}, \text{upper bound} ) \). - Round each value to one decimal place as needed. \[ (\boxed{}, \boxed{}) \] (Round to one decimal place as needed.) 3. **Interpret the Results:** - Select the correct interpretation from the provided choices. - Fill in the answer box to complete the choice with the percentage and confidence interval details. **Choices for Interpretation:** A. \( \boxed{} \% \) of all random samples of six people from the population will have a mean driving distance to work (in miles) that is between the interval's endpoints. B. With \( \boxed{} \% \) confidence, it can be said that most driving distances to work (in miles) in the population are between the interval's endpoints. C. With \( \boxed{} \% \) confidence, it can be said that the population mean driving distance to work (in miles) is between the interval's endpoints. D. It can be said that \( \boxed{} \% \) of the population has a driving distance to work (in miles) that is between the interval's endpoints.
Transcribed Image Text:### Driving Distance Confidence Interval Calculation In a random sample of six people, the mean driving distance to work was 18.8 miles and the standard deviation was 4.5 miles. Assume the population is normally distributed and use the t-distribution to find the margin of error and construct a 90% confidence interval for the population mean \( \mu \). Interpret the results. #### Steps for Calculation: 1. **Identify the Margin of Error:** - Use the dropdown menu to select the appropriate margin of error (MoE). - Round the margin of error to one decimal place as needed. **Margin of Error:** \[ \boxed{} \] (Round to one decimal place as needed.) 2. **Construct a 90% Confidence Interval for the Population Mean:** - Compute the confidence interval using the sample mean and the margin of error. - The interval will be in the form \( ( \text{lower bound}, \text{upper bound} ) \). - Round each value to one decimal place as needed. \[ (\boxed{}, \boxed{}) \] (Round to one decimal place as needed.) 3. **Interpret the Results:** - Select the correct interpretation from the provided choices. - Fill in the answer box to complete the choice with the percentage and confidence interval details. **Choices for Interpretation:** A. \( \boxed{} \% \) of all random samples of six people from the population will have a mean driving distance to work (in miles) that is between the interval's endpoints. B. With \( \boxed{} \% \) confidence, it can be said that most driving distances to work (in miles) in the population are between the interval's endpoints. C. With \( \boxed{} \% \) confidence, it can be said that the population mean driving distance to work (in miles) is between the interval's endpoints. D. It can be said that \( \boxed{} \% \) of the population has a driving distance to work (in miles) that is between the interval's endpoints.
### Driving Distance to Work: Margin of Error and Confidence Interval In a random sample of six people, the mean driving distance to work was 18.8 miles and the standard deviation was 4.5 miles. Assume the population is normally distributed and use the t-distribution to find the margin of error and construct a 90% confidence interval for the population mean \( \mu \). Interpret the results. --- #### Steps to Solve: 1. **Identify the Margin of Error:** - (Round to two decimal places as needed.) 2. **Construct the 90% Confidence Interval for the Population Mean:** - (Round to two decimal places as needed.) 3. **Interpret the Results:** --- #### Multiple Choice Interpretation: Select the choice that correctly interprets the confidence interval. A. With \( \% \) confidence, all random samples of six people from the population will have a mean driving distance to work (in miles) that is between the interval's endpoints. B. With \( \% \) confidence, it can be said that most driving distances to work (in miles) in the population are between the interval's endpoints. C. With \( \% \) confidence, it can be said that the population mean driving distance to work (in miles) is between the interval's endpoints. D. It can be said that \( \% \) of the population has a driving distance to work (in miles) that is between the interval's endpoints. --- #### Detailed Diagram Explanation: Currently, for this task, we do not have a specific diagram or graph to explain. This is a text-based problem where you will compute the margin of error and confidence interval using statistical formulas involving the mean, standard deviation, sample size, and the t-distribution for a 90% confidence level. Make sure to use the appropriate t-value for a 90% confidence interval with a sample size of six, considering the degrees of freedom (df = 5).
Transcribed Image Text:### Driving Distance to Work: Margin of Error and Confidence Interval In a random sample of six people, the mean driving distance to work was 18.8 miles and the standard deviation was 4.5 miles. Assume the population is normally distributed and use the t-distribution to find the margin of error and construct a 90% confidence interval for the population mean \( \mu \). Interpret the results. --- #### Steps to Solve: 1. **Identify the Margin of Error:** - (Round to two decimal places as needed.) 2. **Construct the 90% Confidence Interval for the Population Mean:** - (Round to two decimal places as needed.) 3. **Interpret the Results:** --- #### Multiple Choice Interpretation: Select the choice that correctly interprets the confidence interval. A. With \( \% \) confidence, all random samples of six people from the population will have a mean driving distance to work (in miles) that is between the interval's endpoints. B. With \( \% \) confidence, it can be said that most driving distances to work (in miles) in the population are between the interval's endpoints. C. With \( \% \) confidence, it can be said that the population mean driving distance to work (in miles) is between the interval's endpoints. D. It can be said that \( \% \) of the population has a driving distance to work (in miles) that is between the interval's endpoints. --- #### Detailed Diagram Explanation: Currently, for this task, we do not have a specific diagram or graph to explain. This is a text-based problem where you will compute the margin of error and confidence interval using statistical formulas involving the mean, standard deviation, sample size, and the t-distribution for a 90% confidence level. Make sure to use the appropriate t-value for a 90% confidence interval with a sample size of six, considering the degrees of freedom (df = 5).
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