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Estimation, Confidence Intervals, and Tests Using a Normal Distribution

Estimation, Confidence Intervals, and Tests Using a Normal Distribution
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2018-11-27 19:33
FunctionCoordinate GeometryCalculusProbability & Statistics
In collections Pearson Maths A level Further Statistics 2
This example demonstrates parameter estimation, confidence interval construction, and hypothesis testing using a normal distribution. Key math concepts include normal distribution, sample mean, sample variance, confidence intervals, and hypothesis testing. GeoGebra commands and objects used in construction are Sequence, Point, Integral, Intersect, OrthogonalLine, Segment, Vector, RandomNormal, Sum, and SampleVariance. Suitable for high school and above learners to understand basic statistical inference methods.

GeoGebra Commands & Parameters

  1. Sequence(Segment[(-100, i), (100, i)], i, -50, 50, 1) → list2
  2. Sequence(Segment[(i, -100), (i, 100)], i, -50, 50, 1) → list4
  3. Point(g) → A
  4. Point(g) → B
  5. Integral(f, x(A), x(B)) → b
  6. Intersect(f, i, (-2, 0.12098536225957168)) → D
  7. Intersect(f, h, (2, 0.12098536225957168)) → E
  8. Integral(f, -30, x(B)) → a
  9. OrthogonalLine(D, g) → j
  10. OrthogonalLine(E, g) → l
  11. Intersect(j, g) → C
  12. Intersect(f, l, (2, 0.12098536225957168)) → F
  13. Intersect(l, g) → G
  14. Segment(D, C) → m
  15. Segment(E, G) → n_3
  16. OrthogonalLine(A, g) → p
  17. OrthogonalLine(B, g) → q
  18. Intersect(f, p, (-2.930333438686662, 0.06819101473948343)) → H
  19. Intersect(f, q, (0.847407925433364, 0.1823461932923673)) → I
  20. Segment(H, A) → r
  21. Segment(I, B) → s
  22. Integral(f, ((-k) * σ) + μ, (k * σ) + μ) → o
  23. Intersect(f, f_1, (0, 0.19947114020071635)) → J
  24. Point(f_1) → K
  25. Intersect(j, f_1) → L
  26. Intersect(g, f_1) → M
  27. Vector(M, K) → v
  28. Segment(M, J) → g_1
  29. RandomNormal(μ, σ) → r1
  30. Sequence((RandomNormal[μ, σ], 0), i, 1, n) → l1
  31. Sum(l2) → s1
  32. Segment(P5, X) → h_1
  33. SampleVariance(l2) → w