Find the best answers to your questions at Westonci.ca, where experts and enthusiasts provide accurate, reliable information. Explore a wealth of knowledge from professionals across different disciplines on our comprehensive platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
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.
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.