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:
- What is the relationship between confidence level and margin of error?
- How does increasing the sample size affect the accuracy of a survey?
- What is the formula to calculate sample size for a given confidence level?
- How do confidence intervals change with larger sample sizes?
- 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
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