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Hypothesis Testing for Normal Mean

Hypothesis Testing for Normal Mean
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2014-02-25 19:00
FunctionCalculusProbability & StatisticsSlider AnimationGraphing
In collections Statistics 2
This example demonstrates the process and visualization of hypothesis testing for the mean of a normal distribution. Key math concepts include hypothesis testing, normal distribution, p-value calculation, and standard normal transformation. GeoGebra commands and objects used in the construction include If, RandomNormal, Take, mean, stdevp, Normal, InverseNormal, Integral, and Segment. It is suitable for high school and above students to understand basic statistical inference methods and steps.

GeoGebra Commands & Parameters

  1. If(b ≟ 2, μ - Random[0, 3], If[b ≟ 1, μ + Random[0, 3], μ + Random[-3, 3]]) → μ_1
  2. RandomNormal(μ_1, σ) → A100
  3. RandomNormal(μ_1, σ) → A1
  4. RandomNormal(μ_1, σ) → A99
  5. RandomNormal(μ_1, σ) → A98
  6. RandomNormal(μ_1, σ) → A97
  7. RandomNormal(μ_1, σ) → A96
  8. RandomNormal(μ_1, σ) → A95
  9. RandomNormal(μ_1, σ) → A94
  10. RandomNormal(μ_1, σ) → A93
  11. RandomNormal(μ_1, σ) → A92
  12. RandomNormal(μ_1, σ) → A91
  13. RandomNormal(μ_1, σ) → A90
  14. RandomNormal(μ_1, σ) → A89
  15. RandomNormal(μ_1, σ) → A88
  16. RandomNormal(μ_1, σ) → A87
  17. RandomNormal(μ_1, σ) → A86
  18. RandomNormal(μ_1, σ) → A85
  19. RandomNormal(μ_1, σ) → A84
  20. RandomNormal(μ_1, σ) → A83
  21. RandomNormal(μ_1, σ) → A82
  22. RandomNormal(μ_1, σ) → A81
  23. RandomNormal(μ_1, σ) → A80
  24. RandomNormal(μ_1, σ) → A79
  25. RandomNormal(μ_1, σ) → A78
  26. RandomNormal(μ_1, σ) → A77
  27. RandomNormal(μ_1, σ) → A76
  28. RandomNormal(μ_1, σ) → A75
  29. RandomNormal(μ_1, σ) → A74
  30. RandomNormal(μ_1, σ) → A73
  31. RandomNormal(μ_1, σ) → A72
  32. RandomNormal(μ_1, σ) → A71
  33. RandomNormal(μ_1, σ) → A70
  34. RandomNormal(μ_1, σ) → A69
  35. RandomNormal(μ_1, σ) → A68
  36. RandomNormal(μ_1, σ) → A67
  37. RandomNormal(μ_1, σ) → A66
  38. RandomNormal(μ_1, σ) → A65
  39. RandomNormal(μ_1, σ) → A64
  40. RandomNormal(μ_1, σ) → A63
  41. RandomNormal(μ_1, σ) → A62
  42. RandomNormal(μ_1, σ) → A61
  43. RandomNormal(μ_1, σ) → A60
  44. RandomNormal(μ_1, σ) → A59
  45. RandomNormal(μ_1, σ) → A58
  46. RandomNormal(μ_1, σ) → A57
  47. RandomNormal(μ_1, σ) → A56
  48. RandomNormal(μ_1, σ) → A55
  49. RandomNormal(μ_1, σ) → A54
  50. RandomNormal(μ_1, σ) → A53
  51. RandomNormal(μ_1, σ) → A52
  52. RandomNormal(μ_1, σ) → A51
  53. RandomNormal(μ_1, σ) → A50
  54. RandomNormal(μ_1, σ) → A49
  55. RandomNormal(μ_1, σ) → A48
  56. RandomNormal(μ_1, σ) → A47
  57. RandomNormal(μ_1, σ) → A46
  58. RandomNormal(μ_1, σ) → A45
  59. RandomNormal(μ_1, σ) → A44
  60. RandomNormal(μ_1, σ) → A43
  61. RandomNormal(μ_1, σ) → A42
  62. RandomNormal(μ_1, σ) → A41
  63. RandomNormal(μ_1, σ) → A40
  64. RandomNormal(μ_1, σ) → A39
  65. RandomNormal(μ_1, σ) → A38
  66. RandomNormal(μ_1, σ) → A37
  67. RandomNormal(μ_1, σ) → A36
  68. RandomNormal(μ_1, σ) → A35
  69. RandomNormal(μ_1, σ) → A34
  70. RandomNormal(μ_1, σ) → A33
  71. RandomNormal(μ_1, σ) → A32
  72. RandomNormal(μ_1, σ) → A31
  73. RandomNormal(μ_1, σ) → A30
  74. RandomNormal(μ_1, σ) → A29
  75. RandomNormal(μ_1, σ) → A28
  76. RandomNormal(μ_1, σ) → A27
  77. RandomNormal(μ_1, σ) → A26
  78. RandomNormal(μ_1, σ) → A25
  79. RandomNormal(μ_1, σ) → A24
  80. RandomNormal(μ_1, σ) → A23
  81. RandomNormal(μ_1, σ) → A22
  82. RandomNormal(μ_1, σ) → A21
  83. RandomNormal(μ_1, σ) → A20
  84. RandomNormal(μ_1, σ) → A19
  85. RandomNormal(μ_1, σ) → A18
  86. RandomNormal(μ_1, σ) → A17
  87. RandomNormal(μ_1, σ) → A16
  88. RandomNormal(μ_1, σ) → A15
  89. RandomNormal(μ_1, σ) → A14
  90. RandomNormal(μ_1, σ) → A13
  91. RandomNormal(μ_1, σ) → A12
  92. RandomNormal(μ_1, σ) → A11
  93. RandomNormal(μ_1, σ) → A10
  94. RandomNormal(μ_1, σ) → A9
  95. RandomNormal(μ_1, σ) → A8
  96. RandomNormal(μ_1, σ) → A7
  97. RandomNormal(μ_1, σ) → A6
  98. RandomNormal(μ_1, σ) → A5
  99. RandomNormal(μ_1, σ) → A4
  100. RandomNormal(μ_1, σ) → A3
  101. RandomNormal(μ_1, σ) → A2
  102. Take(L, 1, n) → L_1
  103. mean(L_1) → m
  104. stdevp(L_1) → s
  105. Normal(μ, σ, m) → x_1
  106. InverseNormal(0, 1, significance / 100) → l
  107. Integral(f, -100, l) → a
  108. InverseNormal(0, 1, significance / 200) → l_1
  109. Integral(f, -100, l_1) → d
  110. Segment(A, B) → j
  111. InverseNormal(0, 1, 1 - significance / 100) → l_2
  112. Integral(f, l_2, 100) → c
  113. InverseNormal(0, 1, 1 - significance / 200) → l_3
  114. Integral(f, l_3, 100) → g
  115. If(b ≟ 2, l, If[b ≟ 1, l_2, If[m > 0, l_3, l_1]]) → v
  116. If(b ≟ 2, If[z < v, 1, 0], If[b ≟ 1, If[z > v, 1, 0], If[abs(z) > abs(v), 1, 0]]) → r

AI Drawing Prompt Reference

Create a visualization for hypothesis testing of a normal distribution, featuring a slider to control the mean, generating sample points at different positions based on the slider value, and showing the distribution of sample points and mean line, demonstrating the standard normal transformation and p-value calculation process.
The prompt above was compiled from the original drawing commands and is for reference only.