Hypothesis Testing

Hypothesis testing is a formal procedure for deciding whether sample data provide enough evidence to reject a claim about a population. It is one of the most widely used tools in statistics.

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The Logic of Hypothesis Testing

1. Start with a claim about a population parameter
2. Collect sample data
3. Determine how likely the observed data would be if the claim were true
4. Decide whether to reject or fail to reject the claim

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Step-by-Step Framework

Step 1: State the Hypotheses

Hypothesis	Symbol	Description
Null hypothesis	H₀	The default claim — typically "no effect" or "no difference"
Alternative hypothesis	H₁ (or Hₐ)	The claim you want to test — "there is an effect" or "there is a difference"

Example: A manufacturer claims the mean lifetime of a battery is 500 hours.

H₀: μ = 500
H₁: μ ≠ 500    (two-tailed test)

Step 2: Choose the Significance Level

The significance level (α) is the probability of rejecting H₀ when it is actually true (Type I error). Common choices: