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Hypothesis Tests of the Population Mean

Hypothesis Tests of the Population Mean
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2017-11-11 00:01
Probability & StatisticsGraphing
This example demonstrates the graphical process of hypothesis testing for the population mean. Core mathematical concepts include statistical inference, hypothesis testing, sample mean, standard deviation, and p-value calculation. GeoGebra commands like Sequence, Element, Mod, If, Min are used, along with objects such as CnfSq, OpSq2, Seed, Op2, etc., suitable for high school and above learners to understand the principles and steps of hypothesis testing.

GeoGebra Commands & Parameters

  1. Sequence(Mod[5 + (17 * k), 40] + 1, k, 1, 40) → OpSq2, {23, 40, 17, 34, 11, 28, 5, 22, 39, 16, 33, 10, 27, 4, 21, 38, 15, 32, 9, 26, 3, 20, 37, 14, 31, 8, 25, 2, 19, 36, 13, 30, 7, 24, 1, 18, 35, 12, 29, 6}
  2. Element(OpSq2, Seed) → Op2
  3. Mod(Op2, 8) → Ch3
  4. Sequence(Mod[3 + (23 * k), 40] + 1, k, 1, 40) → OpSq1, {27, 10, 33, 16, 39, 22, 5, 28, 11, 34, 17, 40, 23, 6, 29, 12, 35, 18, 1, 24, 7, 30, 13, 36, 19, 2, 25, 8, 31, 14, 37, 20, 3, 26, 9, 32, 15, 38, 21, 4}
  5. Element(OpSq1, Seed) → Op1
  6. Element(CnfSq, Mod[Op1, 4] + 1) → Cnf
  7. Sequence(Mod[6 + (19 * k), 40] + 1, k, 1, 40) → OpSq3, {26, 5, 24, 3, 22, 1, 20, 39, 18, 37, 16, 35, 14, 33, 12, 31, 10, 29, 8, 27, 6, 25, 4, 23, 2, 21, 40, 19, 38, 17, 36, 15, 34, 13, 32, 11, 30, 9, 28, 7}
  8. Element(OpSq3, Seed) → Op3
  9. Mod(Op3, 2) → Ch2
  10. Element(SzSq, Mod[Seed, 6] + 1) → Size
  11. Element(PrbSq, Ch3 + 1) → TstPrb
  12. If(Ch3 < 4, -1, 1) → DrNmb
  13. Element(XbrSq, Mod[Seed, 6] + 1) → Xbr
  14. Element(StDvSq, Mod[Seed, 6] + 1) → StDv
  15. Element(AcSq, Mod[Seed, 6] + 1) → Acc
  16. If(DrNmb ≟ -1, μ2, μ1) → μ0
  17. Min(PVLT, PVGT) → PVHlf
  18. If(PVHlf < 0.00010, " ", PVEQ) → PVCmp2
  19. If(PVHlf < 0.00010, "< 0.0002", ("= " * PVEQ)) → PVCmp1
  20. If(Ch3 < 2, PVLT, If[Ch3 > 5, PVGT, PVEQ]) → PV
  21. If(PV < 0.00010, "< 0.0002", ("= " * PV)) → PVTx
  22. If(Ch3 < 2, "less than", If[Ch3 > 5, "greater than", "not equal to"]) → IETx
  23. If(Ch3 < 2, "<", If[Ch3 > 5, ">", "≠"]) → IE1
  24. If(Ch3 < 2, "≥", If[Ch3 > 5, "≤", "="]) → IE0
  25. If(Ch3 < 2, "left-tailed", If[Ch3 > 5, "right-tailed", "two-tailed"]) → TstTyp
  26. If(Ch3 < 2, PVLTtxt, If[Ch3 > 5, PVGTtxt, PVEQtxt]) → PVCcl
  27. If(PV < α, "<", "≥") → DcSgn
  28. If(PV < α, "is strong", "is not strong") → DcTx
  29. If(PV < α, "is", "is not") → DcEv
  30. If(μ0 < 0, (("(" * μ0) * ")"), μ0) → MuTx
  31. Element(PSSq, Mod[Seed, 6] + 1) → PS0