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假设检验的功效可视化

假设检验的功效可视化
几何画板及绘图内容加载中，请稍等……
2014-07-22 09:35
解析几何微积分概率统计滑块动画函数图像
所属专题 AP Statistics
①本范例通过可视化展示统计功效的概念，并帮助说明功效、样本量、标准差之间的关系；②涉及的核心数学概念包括假设检验、统计功效、样本量、标准差、正态分布；③作图要点——从下方『构造摘要』提炼用到了 Point, InverseNormal, Normal, Segment, IntegralBetween, Textfield, Vector 等GeoGebra命令/对象；④适合高中及以上学生或统计学初学者学习假设检验与统计功效。

GeoGebra 命令及参数

  1. Point(baseline) → mu1Point
  2. InverseNormal(mu0, sigma0, 1 - alpha / 2) → nullRightThreshold
  3. InverseNormal(mu0, sigma0, alpha / 2) → nullLeftThreshold
  4. Normal(mu0, sigma0, x) → nullDist
  5. Segment((nullLeftThreshold, nullDist(nullLeftThreshold)), (nullLeftThreshold, 0)) → leftThresholdLine
  6. Segment((nullRightThreshold, nullDist(nullRightThreshold)), (nullRightThreshold, 0)) → rightThresholdLine
  7. IntegralBetween(f, baseline, nullLeftThreshold, nullRightThreshold) → T2Region
  8. IntegralBetween(f, baseline, Min[leftBound, mu1 - (4 * sigma1)], nullLeftThreshold) → leftPowerRegion
  9. IntegralBetween(f, baseline, nullRightThreshold, Max[rightBound, mu1 + (4 * sigma1)]) → rightPowerRegion
  10. Textfield(alpha) → alphaInputBox
  11. IntegralBetween(nullDist, 0, leftBound, nullLeftThreshold) → t1lefttail
  12. IntegralBetween(nullDist, 0, nullRightThreshold, rightBound) → t1righttail
  13. Segment((nullLeftThreshold, nullDist(nullLeftThreshold)), (nullLeftThreshold, 0.6)) → leftRejectLine
  14. Segment((nullRightThreshold, nullDist(nullRightThreshold)), (nullRightThreshold, 0.6)) → rightRejectLine
  15. Vector((nullLeftThreshold, 0.55), (nullLeftThreshold - 0.8, 0.55)) → leftRejectArrow
  16. Vector((nullRightThreshold, 0.55), (nullRightThreshold + 0.8, 0.55)) → rightRejectArrow
  17. Textfield(difference) → differenceInputBox
  18. Segment((nullLeftThreshold, 0), (nullLeftThreshold, offset)) → leftThresholdLine2
  19. Segment((nullRightThreshold, 0), (nullRightThreshold, offset)) → rightThresholdLine2
  20. Segment(Point[{mu0, offset - 0.09}], Point[{mu0, offset - 0.11}]) → differenceLineLeftEnd
  21. Segment(Point[{mu1, offset - 0.09}], Point[{mu1, offset - 0.11}]) → differenceLineRightEnd
  22. Segment(Point[{mu0, offset}], Point[{mu0, offset - 0.017}]) → altOriginMark
  23. Segment((mu0, 0), (mu0, offset)) → mu0Guideline
  24. Vector((mu0, offset - 0.1), (mu1, offset - 0.1)) → differenceLine

AI 绘图提示语参考

画一个展示假设检验统计功效的图形，包含两条水平线表示临界值，一个正态分布曲线，以及两个积分区域表示第一类错误和第二类错误。使用滑块调节标准差和样本量，显示不同参数下的功效变化。添加箭头和文本标注说明关键区域和参数。
以上提示语为根据原始绘图命令整理而来，仅供参考。