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Quantitative MethodsModule 7 of 11

Estimation and Inference

5

Concepts

3

Formulas

1

Decisions

3

Quiz Questions

Key Concepts

5 concepts covered in this module.

Simple Random Sampling

Every member of the population has an equal probability of being selected. Foundation of statistical inference.

Stratified Random Sampling

Divide population into subgroups (strata), then sample from each. Ensures representation of all groups.

Central Limit Theorem (CLT)

For n ≥ 30, the sampling distribution of the sample mean is approximately normal, regardless of the population distribution.

Standard Error

SE = σ / √n. Measures the precision of the sample mean as an estimator. Decreases with larger samples.

Confidence Interval

Point estimate ± (Critical value × Standard Error). 95% CI uses z = 1.96 for large samples.

Formulas

3 essential formulas for this module.

Standard Error of Mean

SE = σ / √n (or s / √n if σ unknown)

Where: σ = population SD, n = sample size

Confidence Interval

X̄ ± zα/2 × (σ / √n)

Where: zα/2 = critical value for confidence level

Confidence Interval (t)

X̄ ± tα/2,df × (s / √n)

Where: Used when σ unknown and n < 30; df = n-1

Decision Frameworks

1 decision frameworks to guide your analysis.

z-statistic vs t-statistic?

  • z: population σ known, or n ≥ 30
  • t: population σ unknown AND n < 30

Mind Map

Visual overview of how concepts connect in this module.

Estimation & Inference
Sampling Methods
Simple random
Stratified random
Cluster sampling
Non-probability sampling
Central Limit Theorem
n ≥ 30 for non-normal
X̄ ~ Normal(μ, σ/√n)
Foundation of inference
Confidence Intervals
Point estimate ± margin
z for known σ or large n
t for unknown σ and small n
90%/95%/99% levels
Standard Error
SE = σ/√n
Decreases with more data
Measures precision
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Simple Random Sampling

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Every member of the population has an equal probability of being selected. Foundation of statistical inference.
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