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P-Value and Critical Value Comparison

P-Value and Critical Value Comparison
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2014-03-28 02:16
FunctionGraphing
This example demonstrates the comparison between the critical value approach and the P-value approach in hypothesis testing. It involves core concepts like hypothesis testing, P-values, critical values, and normal distributions. The construction utilizes GeoGebra commands and objects such as Sequence, Append, Element, Mean, Integral, Line, Vector, If, IntegralBetween, and Text to visualize normal curves, sample means, critical values, and P-values. It is suitable for high school and above students learning about statistical methods.

GeoGebra Commands & Parameters

  1. Sequence(k, k, 80, 99) → CL1
  2. Append(CL1, 99.9) → CL2
  3. Element(CL2, cs) → Confidence
  4. Sequence(RandomNormal[μ + Type - 2 + seed, σ], k, 1, size) → Sample
  5. Mean(Sample) → xbar
  6. Integral(BellCurve, TstSt, 10) → PVhi
  7. Integral(BellCurve, -10, TstSt) → PVlo
  8. Line((-5, 0), (5, 0)) → XAx2
  9. Vector(TST2, TSH2) → TSV1
  10. If(Type ≟ 2, (-InverseNormal[0, 1, α / 2]), (-InverseNormal[0, 1, α])) → CVhi
  11. Vector(TST1, TSH1) → TSV2
  12. If(Type ≟ 2, InverseNormal[0, 1, α / 2], InverseNormal[0, 1, α]) → CVlo
  13. Vector(CVT2, CVH2) → CVVhi
  14. Integral(exp((-x^(2))) / ((4 * 3.141592653589793)), TstSt, 10) → Mhix
  15. Integral((x * e^(((-x^(2))) / 2) / sqrt((2 * 3.141592653589793))), TstSt, 10) → Mhiy
  16. Vector(CVT1, CVH1) → CVVlo
  17. Integral(exp((-x^(2))) / ((4 * 3.141592653589793)), -10, TstSt) → Mlox
  18. Integral((x * e^(((-x^(2))) / 2) / sqrt((2 * 3.141592653589793))), -10, TstSt) → Mloy
  19. Vector(A, CMlo) → PVVlo
  20. Vector(B, CMhi) → PVVhi
  21. Element(TypTx, Type) → type
  22. Integral(exp((-x^(2))) / ((4 * 3.141592653589793)), CVhi, 10) → Mhix2
  23. Integral((x * e^(((-x^(2))) / 2) / sqrt((2 * 3.141592653589793))), CVhi, 10) → Mhiy2
  24. Vector(C, CMhi2) → AlphaRV
  25. Integral(exp((-x^(2))) / ((4 * 3.141592653589793)), -10, CVlo) → Mlox2
  26. Integral((x * e^(((-x^(2))) / 2) / sqrt((2 * 3.141592653589793))), -10, CVlo) → Mloy2
  27. Vector(D, CMlo2) → AlphaRCM
  28. Integral(BellCurve, -5, (-abs(TstSt))) → TTLf
  29. Integral(BellCurve, abs(TstSt), 5) → TTRt
  30. Integral(exp((-x^(2))) / ((4 * 3.141592653589793)), -10, (-abs(TstSt))) → Mlox3
  31. Integral((x * e^(((-x^(2))) / 2) / sqrt((2 * 3.141592653589793))), -10, (-abs(TstSt))) → Mloy3
  32. Integral(BellCurve, -10, (-abs(TstSt))) → MTTL
  33. Integral(exp((-x^(2))) / ((4 * 3.141592653589793)), abs(TstSt), 10) → Mhix3
  34. Integral((x * e^(((-x^(2))) / 2) / sqrt((2 * 3.141592653589793))), abs(TstSt), 10) → Mhiy3
  35. Vector(E, CMlo3) → TTLV
  36. Vector(E, CMhi3) → v
  37. Vector(F, CMlo4) → AHLV
  38. Vector(G, CMhi4) → AHHV
  39. Vector(OTSLP, OTSP) → u
  40. Sequence(Segment[(k, (-0.01)), (k, 0)], k, -3, 4) → XTcSq2
  41. Sequence(Text[k, (k - 0.05, (-0.045))], k, -3, 4) → XLbTxSq2
  42. Line((-5, 0.8), (5, 0.8)) → XAx1
  43. Sequence(Segment[(k, 0.79), (k, 0.8)], k, -3, 4) → XTcSq1
  44. Sequence(Text[k, (k - 0.05, 0.755)], k, -3, 4) → XLbTxSq1
  45. IntegralBetween(BellCurve2, 0.8, CVhi, 4.5) → AlFlRt
  46. IntegralBetween(BellCurve2, 0.8, -5, CVlo) → AlFlLf
  47. IntegralBetween(BellCurve2, 0.8, -5, CVlo) → AlHfLf
  48. IntegralBetween(BellCurve2, 0.8, CVhi, 4.5) → AlHfRt
  49. Text("Test Statistic", (TstSt - 0.5, 0.71)) → TSLab2