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Quantitative MethodsModule 8 of 11

Hypothesis Testing

5

Concepts

3

Formulas

1

Decisions

4

Quiz Questions

Key Concepts

5 concepts covered in this module.

Null & Alternative Hypotheses

H0: status quo (what we try to reject). Ha: what we want to prove. We never "accept" H0, only fail to reject.

Type I and Type II Errors

Type I (α): reject true H0 (false positive). Type II (β): fail to reject false H0 (false negative). Power = 1 - β.

Test Statistic

test stat = (sample stat - hypothesized value) / standard error. Compare to critical value.

p-value

Smallest significance level at which H0 would be rejected. Reject H0 if p-value < α.

One-tailed vs Two-tailed

Two-tailed: Ha: μ ≠ value. One-tailed: Ha: μ > value or μ < value. Two-tailed has critical values on both sides.

Formulas

3 essential formulas for this module.

Test Statistic (mean)

t = (X̄ - μ0) / (s / √n)

Where: μ0 = hypothesized mean

Test for Difference in Means

t = (X̄1 - X̄2) / √(s²1/n1 + s²2/n2)

Where: For independent samples

F-test for Variance Equality

F = s²1 / s²2 (larger variance in numerator)

Where: df1 = n1-1, df2 = n2-1

Decision Frameworks

1 decision frameworks to guide your analysis.

Which test to use?

  • t-test: testing means (unknown σ)
  • F-test: testing equality of two variances
  • Chi-square: testing a single variance, contingency tables

Mind Map

Visual overview of how concepts connect in this module.

Hypothesis Testing
Framework
State H0 and Ha
Select test statistic
Specify significance level
State decision rule
Calculate and decide
Errors
Type I: reject true H0 (α)
Type II: fail to reject false H0 (β)
Power = 1 - β
Test Types
t-test for means
F-test for variances
Chi-square for single variance
Parametric vs non-parametric
p-value Approach
p < α: reject H0
p ≥ α: fail to reject
Most common approach
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Null & Alternative Hypotheses

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Answer
H0: status quo (what we try to reject). Ha: what we want to prove. We never "accept" H0, only fail to reject.
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Parametric and Non-Parametric Tests of Independence