https://file.aiquickdraw.com/mathbot/file/1729570055536pmqifu83.jpg

The problem asks you to interpret the 95% confidence interval for the sample proportion. Here's the step-by-step breakdown of how to interpret it:

### Given:
- Sample proportion = 53.2%
- Margin of error = ±7%

The confidence interval can be found by adding and subtracting the margin of error from the sample proportion.

### To find the 95% confidence interval:
- **Lower bound** = 53.2% - 7% = 46.2%
- **Upper bound** = 53.2% + 7% = 60.2%

### Conclusion:
The 95% confidence interval is between **46.2%** and **60.2%**.

This means the researchers estimate with 95% confidence that the true proportion of college students who use dating apps lies between **46.2% and 60.2%**.

Would you like further details on this? Let me know if you have any questions.

Here are 5 related questions to deepen your understanding:

1. What does a 95% confidence level mean in this context?
2. How does increasing the sample size affect the margin of error in a confidence interval?
3. If the confidence level were raised to 99%, how would the interval change?
4. What assumptions must be true for this confidence interval to be valid?
5. How is the margin of error calculated in such a scenario?

**Tip:** The confidence interval gives a range where the true population proportion likely lies, but increasing confidence (e.g., to 99%) usually increases the width of the interval.

Researchers asked a random sample of students at a local college if they ever use dating apps. They found that 53.2% of the sample have a margin of error of ±7%. Interpret the 95% confidence interval.

Learn how to interpret a 95% confidence interval for a sample proportion of 53.2%, with a margin of error of ±7%. This problem covers key statistical concepts including confidence intervals and the margin of error, suitable for Grades 11-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation