Welcome to Westonci.ca, the place where your questions find answers from a community of knowledgeable experts. Explore thousands of questions and answers from a knowledgeable community of experts ready to help you find solutions. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
Explanation:
To find the margin of error and the interval estimate of the number of eligible people under 20 years old who had a driver's license in 1995, we will follow these steps:
1. **Calculate the sample proportion (\( \hat{p} \)) for 1995:**
- Given: \( \hat{p} = 0.639 \)
- Sample size (\( n \)) = 1200
2. **Calculate the standard error (SE):**
\[
SE = \sqrt{\frac{\hat{p} (1 - \hat{p})}{n}}
\]
3. **Find the critical value (\( z \)) for a 95% confidence interval:**
- For a 95% confidence level, \( z \approx 1.96 \)
4. **Calculate the margin of error (ME):**
\[
ME = z \times SE
\]
5. **Calculate the interval estimate:**
\[
\text{Interval estimate} = \hat{p} \pm ME
\]
Let's calculate these step-by-step.
### Step 1: Sample Proportion
\[
\hat{p} = 0.639
\]
### Step 2: Standard Error
\[
SE = \sqrt{\frac{0.639 \times (1 - 0.639)}{1200}}
\]
### Step 3: Critical Value
\[
z = 1.96
\]
### Step 4: Margin of Error
\[
ME = 1.96 \times SE
\]
### Step 5: Interval Estimate
\[
\text{Interval estimate} = \hat{p} \pm ME
\]
Let's do the calculations:
#### Standard Error
\[
SE = \sqrt{\frac{0.639 \times 0.361}{1200}}
\]
\[
SE = \sqrt{\frac{0.230679}{1200}}
\]
\[
SE = \sqrt{0.0001922325}
\]
\[
SE \approx 0.01386
\]
#### Margin of Error
\[
ME = 1.96 \times 0.01386
\]
\[
ME \approx 0.02715
\]
#### Interval Estimate
\[
\text{Lower bound} = \hat{p} - ME = 0.639 - 0.02715 = 0.61185
\]
\[
\text{Upper bound} = \hat{p} + ME = 0.639 + 0.02715 = 0.66615
\]
### Summary
- **Margin of Error (ME):** \( 0.02715 \)
- **Interval Estimate:** \( 0.61185 \) to \( 0.66615 \)
These are the 95% confidence interval estimates for the proportion of eligible people under 20 years old who had a driver's license in 1995.
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.
