S7.3StatisticsStretch

One-Tailed Tests

A one-tailed test checks for a change in one specific direction — an increase OR a decrease, not either. The whole significance level sits in a single tail, and the alternative hypothesis uses > or <.

30 min Video by Zeeshan Zamurred Hypothesis Testing

Edexcel Statistics Y1 — Hypothesis Testing playlist (Zeeshan Zamurred)Watch the full walkthrough before the notes below.

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What you'll be able to do

Recognise when a one-tailed test is appropriate
Write the correct one-sided alternative hypothesis
Carry out a one-tailed binomial test
State a conclusion in context

One direction only

Use a one-tailed test when the question asks specifically whether something has $increased$ or $decreased$ (not just “changed”). The alternative hypothesis is one-sided.

H_{1} : p > p_{0} or H_{1} : p < p_{0}

A single direction (the whole

α

in one tail).

Carrying out the test

Assuming $H_{0}$ , find the probability of the observed (or more extreme) result in the relevant tail. Compare it to the significance level $α$ : if it is smaller, reject $H_{0}$ .

P (X \geq observed) < α \Rightarrow reject H_{0}

For an “increase” test (upper tail).

0.03 < 0.05

, so the result is in the critical region.

Answerreject H₀ — evidence of an increase

Tip — For “has it increased?”, compute the UPPER-tail probability P(X ≥ observed); for “decreased”, the lower tail.

Conclusion in context

Always finish with a contextual sentence: state whether there is sufficient evidence, at the given significance level, to support the claimed increase or decrease.

Formula recap

H_{1} : p > p_{0} or p < p_{0}

One-sided alternative.

P (tail) < α \Rightarrow reject H_{0}

Decision rule.

whole α in one tail

Defining feature.

Common mistakes to avoid

Using a one-tailed test when the question says “changed”.

“Changed” (either direction) needs a two-tailed test.

Splitting α between two tails in a one-tailed test.

The full α goes in the single relevant tail.

Key takeaways

One-tailed: tests a specific direction (H₁ uses > or <).
The whole significance level is in one tail.
Compare the tail probability to α, then conclude in context.

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