Paper II · 4 Random Variables, Distributions & Inference · 4.2 Estimation and testing of hypotheses

4.2.2 Testing of hypotheses: null and alternative hypotheses, errors, level of significance and large sample tests

A test of hypothesis is a rule that uses a sample to reject or not reject a claim (H₀) about a population; for large samples (n ≥ 30) the test statistic Z = (statistic − value under H₀) ÷ standard error is compared with 1.96 / 2.58 (two-tailed) or 1.645 / 2.33 (one-tailed).

  • TGPSC MPSO / ASO · Paper II
  • Advanced level
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Key terms

  • hypothesis
  • statistical hypothesis
  • null hypothesis
  • alternative hypothesis
  • simple hypothesis
  • composite hypothesis
  • critical region
  • acceptance region
  • type I error
  • type II error
  • level of significance
  • size of test
  • power of test
  • one-tailed
  • two-tailed
  • critical value
  • p-value
  • Z test
  • large sample
  • standard error
  • test for mean
  • test for proportion
  • difference of means
  • difference of proportions
  • difference of standard deviations
  • Neyman-Pearson lemma

What this note covers

  1. Core factsFoundation
  2. ExplainedStandard
  3. DeeperAdvanced
  4. Common trapsFoundation
  5. Quick revisionFoundation

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