Treffer

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alle Konfidenzintervalle

einzelne Konfidenzintervalle freirubbeln

Prognoseintervalle zu p_{hypo}

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1. Es wurden 30 Stichproben aus einem Pott mit sehr vielen Perlen gestochen. Der Anteil der gelben Perlen 
    (Treffer) ist die Trefferwahrscheinlichkeit p. Die Zahl der gestochenen Treffer steht in Tabellenspalte D.  
    An den Stellen 31 ... 36 werden je 5, an der Stelle 37 werden alle 30 Stichproben zusammengefasst.
    Die 30 (blauen) + 6 (roten) + 1 (schwarze) relative(n) Trefferhäufigkeit(en) werden als Punkte dargestellt.
2. “einzelne Konfidenzintervalle freirubbeln” sucht vertrauenswürdige Werte für p
3. “alle Konfidenzintervalle” plottet alle aus den relativen Häufigkeiten berechneten Konfidenzintervalle.
4. Im Fenster 2 können Parameter variiert und 30 neue Stichproben gezogen werden.
    Wenn man (Grafik 2) viele Stichproben hintereinander zieht und (in Grafik 1) beobachtet, wie viele 
    Konfidentintervalle das vorgegebene p überdecken, erschließt sich die Bedeutung von Konfidenzintervallen. 

Petra

Manfred

Hannes

Hartmut

Torsten

Caren

Pia

Jürgen

Wienandt

Katharina

Anke

Irina

Dustin

Andrea

Gaby

Noah

Finja

Ronja

Paula

Carina

Cécile

Jakov

Niklas

Süleyman

Tim

Carlo

Moritz

Deniz

Abu

Jana

gruppe 1

gruppe 2

gruppe 3

gruppe 4

gruppe 5

gruppe 6

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30 neue Stichproben

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Stelle

B2: 1
B3: 2
B4: 3
B5: 4
B6: 5
B8: 7
B9: 8
B10: 9
B11: 10
B12: 11
B13: 12
B14: 13
B15: 14
B16: 15
B17: 16
B18: 17
B7: 6
I = Segment((0, 0), (0, 1))
p_{hypo} = 0.25 (slider from 0 to 1, step 0.001)
modell: (0, p_{hypo})
n = CountIf(x > 0, CellRange(E2,E50,"numeric"))
f(x) = If[0 < x < n, p_{hypo}]
X = Sequence(i, i, 1, n)
rh = Sequence(Cell[4, i] / (Cell[3, i] + Cell[4, i]), i, 2, n + 1)
Datenpunkte: (X, rh)
N = Sequence(Cell[3, i] + Cell[4, i], i, 2, n + 1)
nummer = 0 (slider from 0 to n, step 1)
Q: (nummer, p_{hypo})
PIu = Sequence(p_{hypo} - (2 * sqrt(((p_{hypo} * (1 - p_{hypo}))) / N(i))), i, 1, n)
PIo = Sequence(p_{hypo} + (2 * sqrt(((p_{hypo} * (1 - p_{hypo}))) / N(i))), i, 1, n)
imPI_{1} = Sequence(If[PIu(i) ≤ rh(i) ≤ PIo(i), true, false], i, 1, n)
Spur: (nummer, p_{hypo})
KIu = Sequence((rh(i) + 2 / N(i) - (2 * sqrt(1 / (N(i))^(2) + (rh(i) * (1 - rh(i)) / N(i))))) / (1 + 4 / N(i)), i, 1, n)
KIo = Sequence((rh(i) + 2 / N(i) + (2 * sqrt(1 / (N(i))^(2) + (rh(i) * (1 - rh(i)) / N(i))))) / (1 + 4 / N(i)), i, 1, n)
KI = Sequence(Segment[(i, KIu(i)), (i, KIo(i))], i, 1, n)
kija = false
a = false
imPI = Sum(imPI_{1})
Text1 = LaTeX(imPI, true, true)
PI = Sequence(Segment[(i, Max[-1, PIu(i)]), (i, Min[2, PIo(i)])], i, 1, n)
B19: 18
B20: 19
B21: 20
B22: 21
B23: 22
B24: 23
B25: 24
B26: 25
B27: 26
B28: 27
B29: 28
B30: 29
B31: 30
M = Sum(CellRange(D2,D40,"numeric"))
L = Sum(CellRange(C2,C40,"numeric"))
Load: round(M / (L + M), 3)
b = false
c = true
μ = NaN
μ_{Stichprobe} = 70 (slider from 10 to 100, step 1)
σ_{Stichprobe} = 30 (slider from 10 to 40, step 1)
p_{Treffer} = 0.25 (slider from 0.1 to 0.9, step 0.05)
E2 = Max(ceil(RandomNormal[μ_{Stichprobe}, σ_{Stichprobe}]), 10)
C2 = RandomBinomial(E2, 1 - p_{Treffer})
D2: E2 - C2
E3 = Max(ceil(RandomNormal[μ_{Stichprobe}, σ_{Stichprobe}]), 10)
C3 = RandomBinomial(E3, 1 - p_{Treffer})
D3: E3 - C3
E4 = Max(ceil(RandomNormal[μ_{Stichprobe}, σ_{Stichprobe}]), 10)
C4 = RandomBinomial(E4, 1 - p_{Treffer})
D4: E4 - C4
E5 = Max(ceil(RandomNormal[μ_{Stichprobe}, σ_{Stichprobe}]), 10)
C5 = RandomBinomial(E5, 1 - p_{Treffer})
D5: E5 - C5
E6 = Max(ceil(RandomNormal[μ_{Stichprobe}, σ_{Stichprobe}]), 10)
C6 = RandomBinomial(E6, 1 - p_{Treffer})
D6: E6 - C6
E7 = Max(ceil(RandomNormal[μ_{Stichprobe}, σ_{Stichprobe}]), 10)
C7 = RandomBinomial(E7, 1 - p_{Treffer})
D7: E7 - C7
E8 = Max(ceil(RandomNormal[μ_{Stichprobe}, σ_{Stichprobe}]), 10)
C8 = RandomBinomial(E8, 1 - p_{Treffer})
D8: E8 - C8
E9 = Max(ceil(RandomNormal[μ_{Stichprobe}, σ_{Stichprobe}]), 10)
C9 = RandomBinomial(E9, 1 - p_{Treffer})
D9: E9 - C9
E10 = Max(ceil(RandomNormal[μ_{Stichprobe}, σ_{Stichprobe}]), 10)
C10 = RandomBinomial(E10, 1 - p_{Treffer})
D10: E10 - C10
E11 = Max(ceil(RandomNormal[μ_{Stichprobe}, σ_{Stichprobe}]), 10)
C11 = RandomBinomial(E11, 1 - p_{Treffer})
D11: E11 - C11
E12 = Max(ceil(RandomNormal[μ_{Stichprobe}, σ_{Stichprobe}]), 10)
C12 = RandomBinomial(E12, 1 - p_{Treffer})
D12: E12 - C12
E13 = Max(ceil(RandomNormal[μ_{Stichprobe}, σ_{Stichprobe}]), 10)
C13 = RandomBinomial(E13, 1 - p_{Treffer})
D13: E13 - C13
E14 = Max(ceil(RandomNormal[μ_{Stichprobe}, σ_{Stichprobe}]), 10)
C14 = RandomBinomial(E14, 1 - p_{Treffer})
D14: E14 - C14
E15 = Max(ceil(RandomNormal[μ_{Stichprobe}, σ_{Stichprobe}]), 10)
C15 = RandomBinomial(E15, 1 - p_{Treffer})
D15: E15 - C15
E16 = Max(ceil(RandomNormal[μ_{Stichprobe}, σ_{Stichprobe}]), 10)
C16 = RandomBinomial(E16, 1 - p_{Treffer})
D16: E16 - C16
E17 = Max(ceil(RandomNormal[μ_{Stichprobe}, σ_{Stichprobe}]), 10)
C17 = RandomBinomial(E17, 1 - p_{Treffer})
D17: E17 - C17
E18 = Max(ceil(RandomNormal[μ_{Stichprobe}, σ_{Stichprobe}]), 10)
C18 = RandomBinomial(E18, 1 - p_{Treffer})
D18: E18 - C18
E19 = Max(ceil(RandomNormal[μ_{Stichprobe}, σ_{Stichprobe}]), 10)
C19 = RandomBinomial(E19, 1 - p_{Treffer})
D19: E19 - C19
E20 = Max(ceil(RandomNormal[μ_{Stichprobe}, σ_{Stichprobe}]), 10)
C20 = RandomBinomial(E20, 1 - p_{Treffer})
D20: E20 - C20
E21 = Max(ceil(RandomNormal[μ_{Stichprobe}, σ_{Stichprobe}]), 10)
C21 = RandomBinomial(E21, 1 - p_{Treffer})
D21: E21 - C21
E22 = Max(ceil(RandomNormal[μ_{Stichprobe}, σ_{Stichprobe}]), 10)
C22 = RandomBinomial(E22, 1 - p_{Treffer})
D22: E22 - C22
E23 = Max(ceil(RandomNormal[μ_{Stichprobe}, σ_{Stichprobe}]), 10)
C23 = RandomBinomial(E23, 1 - p_{Treffer})
D23: E23 - C23
E24 = Max(ceil(RandomNormal[μ_{Stichprobe}, σ_{Stichprobe}]), 10)
C24 = RandomBinomial(E24, 1 - p_{Treffer})
D24: E24 - C24
E25 = Max(ceil(RandomNormal[μ_{Stichprobe}, σ_{Stichprobe}]), 10)
C25 = RandomBinomial(E25, 1 - p_{Treffer})
D25: E25 - C25
E26 = Max(ceil(RandomNormal[μ_{Stichprobe}, σ_{Stichprobe}]), 10)
C26 = RandomBinomial(E26, 1 - p_{Treffer})
D26: E26 - C26
E27 = Max(ceil(RandomNormal[μ_{Stichprobe}, σ_{Stichprobe}]), 10)
C27 = RandomBinomial(E27, 1 - p_{Treffer})
D27: E27 - C27
E28 = Max(ceil(RandomNormal[μ_{Stichprobe}, σ_{Stichprobe}]), 10)
C28 = RandomBinomial(E28, 1 - p_{Treffer})
D28: E28 - C28
E29 = Max(ceil(RandomNormal[μ_{Stichprobe}, σ_{Stichprobe}]), 10)
C29 = RandomBinomial(E29, 1 - p_{Treffer})
D29: E29 - C29
E30 = Max(ceil(RandomNormal[μ_{Stichprobe}, σ_{Stichprobe}]), 10)
C30 = RandomBinomial(E30, 1 - p_{Treffer})
D30: E30 - C30
E31 = Max(ceil(RandomNormal[μ_{Stichprobe}, σ_{Stichprobe}]), 10)
C31 = RandomBinomial(E31, 1 - p_{Treffer})
D31: E31 - C31
C32 = Sum(CellRange(C2,C6,"numeric"))
C33 = Sum(CellRange(C7,C11,"numeric"))
C34 = Sum(CellRange(C12,C16,"numeric"))
C35 = Sum(CellRange(C17,C21,"numeric"))
D32 = Sum(CellRange(D2,D6,"numeric"))
D33 = Sum(CellRange(D7,D11,"numeric"))
D34 = Sum(CellRange(D12,D16,"numeric"))
D35 = Sum(CellRange(D17,D21,"numeric"))
E32 = Sum(CellRange(E2,E6,"numeric"))
E33 = Sum(CellRange(E7,E11,"numeric"))
E34 = Sum(CellRange(E12,E16,"numeric"))
E35 = Sum(CellRange(E17,E21,"numeric"))
KIalle = Sequence(Segment[(i, KIu(i)), (i, KIo(i))], i, n, n)
C36 = Sum(CellRange(C22,C26,"numeric"))
C37 = Sum(CellRange(C27,C31,"numeric"))
C38 = Sum(CellRange(C2,C31,"numeric"))
D36 = Sum(CellRange(D22,D26,"numeric"))
D37 = Sum(CellRange(D27,D31,"numeric"))
D38 = Sum(CellRange(D2,D31,"numeric"))
E36 = Sum(CellRange(E22,E26,"numeric"))
E37 = Sum(CellRange(E27,E31,"numeric"))
E38 = Sum(CellRange(E2,E31,"numeric"))
KIeinzel = Sequence(Segment[(i, KIu(i)), (i, KIo(i))], i, 1, n - 7)
KIgruppen = Sequence(Segment[(i, KIu(i)), (i, KIo(i))], i, n - 6, n - 1)
Peinzel = Take(Datenpunkte, 1, n - 5)
Pgruppen = Take(Datenpunkte, n - 6, n - 1)
Pkomplett = Take(Datenpunkte, n, n)
B32: 31
B33: 32
B34: 33
B35: 34
B36: 35
B37: 36
B38: 37