Module 6: Confidence Intervals & Sample Size
Learn to construct confidence intervals and determine appropriate sample sizes
Prerequisites: Modules 4 & 5
This module builds on concepts from Module 4: The Normal Distribution (z-scores, normal probabilities, t-distribution) and Module 5: Sampling Distributions (Central Limit Theorem, standard error, sampling variability). Make sure you're comfortable with these topics before starting.
Learning Objectives
By the end of this module, you will be able to:
- Explain what a confidence interval is and what it represents
- Distinguish between point estimates and interval estimates
- Interpret confidence levels (90%, 95%, 99%) correctly
- Construct confidence intervals for population means using the t-distribution
- Construct confidence intervals for population proportions
- Determine when to use z vs t distributions for confidence intervals
- Calculate margin of error and understand factors that affect it
- Determine appropriate sample sizes for desired precision
- Interpret confidence intervals correctly (common misconceptions)
Lessons
Introduction to Confidence Intervals
Learn what confidence intervals are, how to interpret them, and why we use them instead of point estimates.
- Point estimates vs. interval estimates
- What is a confidence interval?
- Confidence level (90%, 95%, 99%)
- Margin of error
- Correct vs. incorrect interpretations
Confidence Intervals for Means
Master constructing confidence intervals for population means using the t-distribution.
- CI formula for means: x̄ ± t* × (s/√n)
- t-distribution and degrees of freedom
- When to use z vs t distributions
- Finding critical values from t-table
- Effect of confidence level on interval width
Confidence Intervals for Proportions
Learn to construct and interpret confidence intervals for population proportions.
- CI formula for proportions: p̂ ± z* × √(p̂(1-p̂)/n)
- Success-failure condition: np̂ ≥ 10 and n(1-p̂) ≥ 10
- Critical z-values (1.645, 1.96, 2.576)
- Calculating and interpreting proportion CIs
Determining Sample Size
Learn how to calculate the sample size needed to achieve a desired margin of error.
- Why sample size matters
- Sample size for estimating means: n = (z*σ/E)²
- Sample size for estimating proportions: n = p̂(1-p̂)(z*/E)²
- Conservative estimate: p̂ = 0.5
- Trading off precision vs. cost
Assessments & Practice
Test your understanding and practice what you've learned.
Study Tips for Module 6
- Master the interpretation: Know what a confidence interval DOES and DOES NOT tell you
- Practice calculations: Work through many examples to get comfortable with the formulas
- Check conditions: Always verify conditions before constructing CIs (success-failure for proportions, sample size for means)
- Understand t vs z: Know when to use each distribution (σ known vs unknown)
- Sample size trade-offs: Larger samples give narrower intervals but cost more
- Use the study guide: Keep the formula sheet handy when practicing