Module 6 Quick Reference – Formula Sheet

CI for Population Mean (μ)

x̄ ± t* × (s/√n)

Use when σ is unknown
df = n - 1
Find t* from t-table
Standard Error: SE = s/√n

CI for Population Proportion (p)

p̂ ± z* × √(p̂(1-p̂)/n)

Check: np̂ ≥ 10 AND n(1-p̂) ≥ 10
Use z-distribution (not t)
SE = √(p̂(1-p̂)/n)

Sample Size for Mean

n = (z*σ / E)²

E = desired margin of error
σ = estimated population SD
Always round UP

Sample Size for Proportion

n = p̂(1-p̂) × (z*/E)²

No prior estimate? Use p̂ = 0.5
Conservative: n = 0.25(z*/E)²
Always round UP

Margin of Error = (Critical Value) × (Standard Error)

Critical z-Values (Proportions)

Confidence	z*
90%	1.645
95%	1.960
99%	2.576

Common t-Values (Means)

df	90%	95%	99%
10	1.812	2.228	3.169
20	1.725	2.086	2.845
30	1.697	2.042	2.750
∞	1.645	1.960	2.576

Key Conditions & Rules

For t-distribution: Use when σ unknown
Degrees of freedom: df = n - 1
Success-failure: np̂≥10, n(1-p̂)≥10

Sample size: Always round UP
Cut E in half: Multiply n by 4
Higher confidence: Wider interval

Correct CI Interpretation

"We are [confidence level]% confident that the true [parameter] is between [lower] and [upper]."

WRONG: "There's a [confidence]% chance the parameter is in the interval."

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