Math Problem Statement

In general, as the sample size (n) increases...

Group of answer choices

The confidence interval is unaffected

The confidence interval becomes less accurate

The confidence interval gets narrower

The confidence interval gets wider

Solution

The correct choice is:

The confidence interval gets narrower.

As the sample size (n) increases, the standard error decreases, leading to a narrower confidence interval. This means that the estimate becomes more precise, giving a better idea of the true population parameter.

Would you like more details or have any questions?

Here are five related questions for further exploration:

  1. How does the standard error relate to the confidence interval?
  2. What factors other than sample size can influence the width of a confidence interval?
  3. How does the confidence level (e.g., 95%) affect the confidence interval?
  4. What is the impact of variability in the data on the confidence interval?
  5. How does increasing the sample size affect the margin of error in a confidence interval?

Tip: Increasing the sample size improves the precision of estimates but be mindful of diminishing returns, as very large samples can be costly and may not yield proportionally narrower confidence intervals.

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Math Problem Analysis

Mathematical Concepts

Statistics
Confidence Intervals

Formulas

Standard Error formula

Theorems

Central Limit Theorem

Suitable Grade Level

Advanced High School