In a survey of 2480​ golfers, 15% said they were​ left-handed. The​ survey's margin of error was​ 3%. Construct  a confidence interval for the proportion of​ left-handed golfers.
Question content area bottom
Part 1
A.
​(0.11,0.19)
B.
​(0.18,0.21)
C.
​(0.12,0.15)
D.
​(0.12,0.18)

To construct a confidence interval for the proportion of left-handed golfers, we use the given dataTo construct a confidence interval for the proportion of left-handed golfers, we use the given 

- Sample proportion (\( \hat{p} \)): \( 0.15 \) (since 15% of 2480 golfers are left-handed)
- Margin of error (ME): \( 0.03 \) (given as 3%)

The confidence interval (CI) is calculated as follows:

\[
\text{CI} = \left( \hat{p} - \text{ME}, \hat{p} + \text{ME} \right)
\]

Substituting the values:

\[
\text{CI} = \left( 0.15 - 0.03, 0.15 + 0.03 \right) = \left( 0.12, 0.18 \right)
\]

So, the correct answer is:

**D. \((0.12, 0.18)\)**

Would you like more details or have any questions?

---

Here are some additional questions related to confidence intervals:

1. What is the interpretation of a 95% confidence interval in statistics?
2. How does sample size affect the margin of error in a confidence interval?
3. What is the formula for calculating the margin of error in a proportion confidence interval?
4. How does increasing the confidence level affect the width of the confidence interval?
5. What assumptions must be met for constructing a confidence interval for a proportion?
6. How would the confidence interval change if the margin of error was reduced?
7. Can you explain the difference between a confidence interval and a prediction interval?
8. How would you calculate the necessary sample size to achieve a specific margin of error?

**Tip:** Remember that the confidence interval gives a range within which we expect the true population proportion to lie, with a certain level of confidence (e.g., 95%).

Learn how to construct a confidence interval for the proportion of left-handed golfers using statistical methods. This problem involves calculating a confidence interval based on survey data with a margin of error, providing a range within which the true proportion of left-handed golfers is expected to lie. Suitable for advanced high school students and beyond.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation