Null and Alternative Hypotheses

Hypothesis Testing

Uses statistical tests to determine whether an observed difference between samples is statistically significant.

Null Hypothesis (H₀)

States there is no difference between a population parameter and the hypothesized value.

Alternative Hypothesis (Hₐ)

States the population parameter is smaller, greater, or different from the hypothesized value.

Steps for Formulating Hypotheses

1. Identify parameter, 2. Identify claim, 3. Translate to symbols, 4. Formulate H₀ then Hₐ.

Equality Component Rule

H₀ always contains an equality component (=, ≤, ≥); Hₐ never contains an equality sign.

Two-Tailed Hypotheses Form

H₀: μ = k and Hₐ: μ ≠ k

Right-Tailed Hypotheses Form

H₀: μ ≤ k (or μ = k) and Hₐ: μ > k

Left-Tailed Hypotheses Form

H₀: μ ≥ k (or μ = k) and Hₐ: μ < k

Symbol for 'is equal to' / 'has not changed'

=

Symbol for 'is not equal to' / 'has changed'

≠

Symbol for 'greater than' / 'increased'

>

Symbol for 'less than' / 'decreased'

<

Symbol for 'at least' / 'not less than'

≥

Symbol for 'at most' / 'not more than'

≤

Two-Tailed Test

Nondirectional test; extreme test statistics in either tail lead to rejection of H₀.

Right-Tailed Test

One-tailed directional test; tests whether the parameter is greater than the hypothesized value.

Left-Tailed Test

One-tailed directional test; tests whether the parameter is less than the hypothesized value.

Illustrative Example: Residential Lot Price Claim

Claim: μ > ₱15,000; H₀: μ ≤ ₱15,000 (or μ = ₱15,000); Hₐ: μ > ₱15,000.

Illustrative Example: Fitness Center Weight Loss

Claim: μ < 13 pounds; H₀: μ ≥ 13 (or μ = 13); Hₐ: μ < 13.

Illustrative Example: Family Net Worth

Claim: μ ≥ ₱730,000; H₀: μ ≥ ₱730,000; Hₐ: μ < ₱730,000.

Additional Exercise: Dietary Supplement Test

H₀: μ ≤ 15, Hₐ: μ > 15 (Right-tailed test).

Additional Exercise: Sleep Aid Test

H₀: μ ≤ 1, Hₐ: μ > 1 (Right-tailed test).