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Hypothesis Testing

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  Edexcel IAL Statistics 2 (WST02)

Hypothesis Testing

The big idea: A hypothesis test asks: if H₀ were true, how unlikely is a result this extreme? If it is less likely than the significance level, reject H₀.

Summary — What This Chapter Covers
  • Census vs sample; sampling frame; statistic; sampling distribution.
  • Critical region: the values of the test statistic that lead to rejecting H₀.
  • Actual significance level: the true probability of the critical region under H₀.
  • Tests for a binomial p and a Poisson mean λ, one- and two-tailed.
1. Populations, Samples and Sampling Distributions
Sampling

Words that earn marks

Know the definitions: population, census, sample, sampling unit, sampling frame, statistic, sampling distribution.

2. Critical Regions and Significance Levels
Critical regions

Using the tables

For a one-tailed test at 5%, find the largest region whose probability under H₀ does not exceed 0.05.

Worked Example

X ~ B(20, p). Test H₀: p = 0.3 against H₁: p > 0.3 at 5%. Find the critical region and the actual significance level.

3. Tests for a Binomial Proportion and a Poisson Mean
Tests

Conclusion in context

Memorise
Hypotheses

About the parameter p or λ

One-tailed

Whole α in one tail

Two-tailed

α/2 in each tail

Conclusion

In context, not just "reject H₀"

Common Mistakes
Hypotheses in words only
No context
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More Statistics 2 topics

The Binomial and Poisson Distributions
The binomial distribution
Probability density functions
The continuous uniform distribution
Populations, samples and sampling distributions
The Poisson distribution
Continuous Random Variables
Cumulative distribution functions
Normal approximations to the binomial and Poisson
Critical regions and significance levels