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Examples of using the test statistics to test hypotheses

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Test Statistics

(The test numbering matches the numbering in the book "100 Statistical Tests 3rd Edition" by Gopal K Kanji)

Z-test for a population mean (variance known)

  • Sample Size n=5
  • Sample Size n=20
  • Sample Size n=100

Z-test for two population means (variances known and unequal)

  • μ1 = μ2 = 10, σ1 = σ2 = 4
    • n1=10, n2=5
    • n1=20, n2=40
    • n1=200, n2=100
  • μ1 = 15, μ2 = 10, σ1 = 2, σ2 = 4
    • n1=10, n2=5
    • n1=20, n2=40
    • n1=200, n2=100

Z-test for a proportion (binomial distribution)

  • Sample Size n=40
  • Sample Size n=200
  • Sample Size n=1000

Z-test for the equality of two proportions (binomial distribution)

  • n1=40, n2=100
  • n1=200, n2=400
  • n1=1000, n2=500

t-test for a population mean (variance unknown)

  • Sample Size n=5
  • Sample Size n=20
  • Sample Size n=100

t-test for two population means (variances unknown but equal)

  • μ1 = μ2 = 10, σ1 = σ2 = 3
    • n1=10, n2=5
    • n1=20, n2=40
    • n1=200, n2=100
  • μ1 = 12, μ2 = 10, σ1 = σ2 = 3
    • n1=10, n2=5
    • n1=20, n2=40
    • n1=200, n2=100

t-test for two population means (variances unknown and unequal)

  • μ1 = μ2 = 10, σ1 = 2, σ2 = 4
    • n1=10, n2=5
    • n1=20, n2=40
    • n1=200, n2=100
  • μ1 = 20, μ2 = 15, σ1 = 2, σ2 = 4
    • n1=10, n2=5
    • n1=20, n2=40
    • n1=200, n2=100

χ2-test for a population variance

  • Sample Size n=5
  • Sample Size n=20
  • Sample Size n=100

F-test for two population variances (variance ratio test)

  • μ1 = 10, μ2 = 15, σ1 = σ2 = 2
    • n1=10, n2=5
    • n1=20, n2=40
    • n1=200, n2=100

F-test for K population means (analysis of variance)

  • μ1 = μ2 = μ3 = μ4 = 10

    • n1=5, n2=10, n3=15, n4=20
    • n1=50, n2=100, n3=150, n4=200
  • μ1 = 25, μ2 = 20, μ3 = 15, μ4 = 10

    • n1=5, n2=10, n3=15, n4=20

License

This project is available under the MIT license © Nail Sharipov