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MathidiaMathematics Academy
Hypothesis testing
Lesson 56 of 75
Introduction

Null and alternative hypotheses

Objective. Write hypotheses about a population parameter.

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  2. 2. Worked example
  3. 3. Practice
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Learn: the key idea

A hypothesis test begins by writing a null hypothesis H₀, which states the assumed value of a population parameter, and an alternative hypothesis H₁, which states what we suspect instead. For a binomial parameter p, you might write H₀: p=0.5 against H₁: p<0.5 for a one-tailed test, or H₁: p≠0.5 for a two-tailed test. The hypotheses must be about the population parameter, not the sample statistic, and H₁ reflects the direction suggested by the context or claim being tested.

Worked example

A test claims a coin is biased towards tails. Write suitable null and alternative hypotheses for this test.

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Illustrated card showing ?
  1. 1Null hypothesis assumes the coin is fair
  2. 2H₀: p=0.5 where p is probability of tails
  3. 3Claim suggests bias towards tails, a one-tailed alternative
  4. 4H₁: p>0.5

Answer: H₀: p=0.5, H₁: p>0.5

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Common mistake. Students write hypotheses about the sample proportion rather than the population parameter, e.g. H₀: x̄=0.5 instead of H₀: p=0.5. Always express both hypotheses using the population parameter symbol.

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