An insurance company checks police records on 579 accidents selected at random and notes that teenager were at the wheel in 95 of them. Complete parts a) through d). ● ... a) Construct the 95% confidence interval for the percentage of all auto accidents that involve teenage drivers 95% CI= (%%) (Round to one decimal place as needed.)

MATLAB: An Introduction with Applications
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### Constructing a 95% Confidence Interval for Teenage Drivers in Auto Accidents

An insurance company examines police records for a sample of 579 auto accidents selected at random. The records reveal that teenagers were driving in 95 of these accidents. Based on this data, our task is to complete parts (a) through (d).

#### a) Confidence Interval Calculation

To estimate the percentage of all auto accidents involving teenage drivers, we need to construct a 95% confidence interval (CI).

#### **Formula:**
The 95% confidence interval is calculated using the formula:

\[ 
95\% \text{ CI} = [\_\_\_ \%, \_\_\_ \%]
\]

- **Note:** Ensure to round your final answers to one decimal place as needed.

This exercise requires you to determine the confidence interval that will reflect the percentage estimate of teenage involvement in auto accidents accurately, using appropriate statistical methods.

#### Instructions:
- Calculate the sample proportion for teenage drivers.
- Use the sample proportion to compute the standard error.
- Apply the margin of error for a 95% CI using the critical value.
- Substitute these into the formula above to complete the confidence interval estimation. 

Please refer to the resources provided below for additional guidance and examples:
- **View an example**
- **Get more help** 

Finally, verify your calculated interval using the provided option to clear or check your answer.
Transcribed Image Text:### Constructing a 95% Confidence Interval for Teenage Drivers in Auto Accidents An insurance company examines police records for a sample of 579 auto accidents selected at random. The records reveal that teenagers were driving in 95 of these accidents. Based on this data, our task is to complete parts (a) through (d). #### a) Confidence Interval Calculation To estimate the percentage of all auto accidents involving teenage drivers, we need to construct a 95% confidence interval (CI). #### **Formula:** The 95% confidence interval is calculated using the formula: \[ 95\% \text{ CI} = [\_\_\_ \%, \_\_\_ \%] \] - **Note:** Ensure to round your final answers to one decimal place as needed. This exercise requires you to determine the confidence interval that will reflect the percentage estimate of teenage involvement in auto accidents accurately, using appropriate statistical methods. #### Instructions: - Calculate the sample proportion for teenage drivers. - Use the sample proportion to compute the standard error. - Apply the margin of error for a 95% CI using the critical value. - Substitute these into the formula above to complete the confidence interval estimation. Please refer to the resources provided below for additional guidance and examples: - **View an example** - **Get more help** Finally, verify your calculated interval using the provided option to clear or check your answer.
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