Math Problem Statement

The user appears to be working on constructing a confidence interval for a population proportion and interpreting the results.

Solution

From the image, you appear to be working on constructing a confidence interval and interpreting results. Here's a breakdown of the question:

  1. Procedure Name: Based on the problem's requirements, it seems you've correctly identified the "1-Proportion Z-Interval." This method is used when estimating population proportions with a large sample size.

  2. Interval and Point Estimate:

    • The point estimate (p^\hat{p}) is calculated as 4633350\frac{463}{3350}. p^=46333500.1382\hat{p} = \frac{463}{3350} \approx 0.1382
    • The confidence interval for pp is given as 0.1260.126 to 0.1510.151.
  3. Conclusion:

    • Confidence intervals are interpreted as: "We are [confidence level, typically 95%] confident that the true population proportion lies between the lower and upper bounds of the interval."

If you'd like help recalculating values or additional details, let me know!

Related Questions

  1. How is the standard error for a proportion calculated?
  2. What factors determine the width of a confidence interval?
  3. How does sample size impact the reliability of a confidence interval?
  4. Why do we use a Z-interval instead of a T-interval for proportions?
  5. How would increasing the confidence level affect the interval?

Tip

Confidence intervals always provide a range for the parameter (e.g., a population proportion) based on sample data. Their accuracy depends on the sample size and confidence level.

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Math Problem Analysis

Mathematical Concepts

Confidence Intervals
Population Proportions
Statistical Estimation

Formulas

Point Estimate (p̂) = x / n
Confidence Interval for Proportion = p̂ ± Z * sqrt(p̂(1 - p̂)/n)

Theorems

Central Limit Theorem
Properties of Normal Distribution

Suitable Grade Level

Undergraduate Statistics (or Advanced High School)