Math Problem Statement

The larger the level of confidence you desire, the Blank______ the sample size you require.

Multiple choice question.

smaller

larger

Solution

The correct answer is:

larger

Explanation:

To achieve a higher level of confidence in statistical results, you need to reduce the margin of error, which requires a larger sample size. This ensures that the sample more accurately represents the population.


Would you like more details or have any questions?
Here are 5 related questions to explore this topic:

  1. What is the relationship between confidence level and margin of error?
  2. How does increasing the sample size affect the accuracy of a survey?
  3. What is the formula to calculate sample size for a given confidence level?
  4. How do confidence intervals change with larger sample sizes?
  5. What are common confidence levels used in statistics, and why?

Tip: Always calculate the required sample size during study design to ensure statistical reliability.

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Math Problem Analysis

Mathematical Concepts

Statistics
Confidence Levels
Sample Size

Formulas

n = (Z^2 * p * (1-p)) / E^2
Margin of Error = Z * (σ / √n)

Theorems

Central Limit Theorem
Properties of Confidence Intervals

Suitable Grade Level

Grades 11-12 or Undergraduate Level