K:\EKV\PBM_BBS\40_GYV_Projekte\10_Lambacher_Schweizer\P048_15850_LS_SII_NW_22\735481_LS_Qualiphase_LK_SB\03_Beilagen\01_Red\04_Medien\Kap_10 Assets\fertig bearbeitete von Anna\Prognose_Konfidenzintervall_Tool

n->

p->

h->

Prognoseintervall

Konfidenzintervall

Näherung

exakt

Funktionsgleichungen

© Wolfgang Riemer und Ernst Klett Verlag GmbH, Stuttgart 2024

h

Länge

Länge

p

B7: 0.500
c = 2 (slider from 1 to 3, step 0.01)
n = 400 (slider from 1 to 4000, step 1)
B1: n
n_{1}: n
B2: 0.5
A = (0, 0)
B = (1, 0)
f_-(x) = x - (c * sqrt(((x * (1 - x))) / n_{1}))
f_+(x) = x + (c * sqrt(((x * (1 - x))) / n_{1}))
p: (B2, 0)
l = Segment((x(p), 0), (x(p), 1))
m = Segment((x(p), f_-(x(p))), (x(p), f_+(x(p))))
d(x) = If[0 < x < 1, x]
laplace_u: 0.5 - sqrt(0.25 - 9 / B1)
laplace_o: 0.5 + sqrt(0.25 - 9 / B1)
ff_+(x) = If[laplace_u < x < laplace_o, x + (c * sqrt(((x * (1 - x))) / n_{1}))]
ff_-(x) = If[laplace_u < x < laplace_o, x - (c * sqrt(((x * (1 - x))) / n_{1}))]
h: (0, B7)
relHfgk: B7
C = Intersect(relHfgk, f_+, (0.4502481405176315, 0.5))
E = Intersect(relHfgk, f_-, (0.5497518594823685, 0.5))
g = Segment(C, E)
a = Integral(exp(((-x^(2))) / 2) / ((sqrt((2 * pi)) * abs(1))), (-c), c)
Text1: "" + ((a * 100)) + " %"
ho = Segment(h, (1, y(h)))
WALD_{links}: B$7 - (c * sqrt(((B$7 * (1 - B$7))) / n_{1}))
WALD_{rechts}: B$7 + (c * sqrt(((B$7 * (1 - B$7))) / n_{1}))
WILSON_{links}: (c^(2) / ((2 * n_{1})) + relHfgk - (c * sqrt(c^(2) / ((4 * n_{1}^(2))) + ((relHfgk * (1 - relHfgk))) / n_{1}))) / (c^(2) / n_{1} + 1)
WILSON_{rechts}: (c^(2) / ((2 * n_{1})) + relHfgk + (c * sqrt(c^(2) / ((4 * n_{1}^(2))) + ((relHfgk * (1 - relHfgk))) / n_{1}))) / (c^(2) / n_{1} + 1)
WALD: "[ " + (LaTeX[WALD_{links}]) + "; " + (LaTeX[WALD_{rechts}]) + "]"
P_{pinKI}: (x(p), y(h))
PI_{links}: f_-(B2)
PI_{rechts}: f_+(B2)
PI_{NaeherungL}: B2 - c / 2 / sqrt(B1)
PI_{NaeherungR}: B2 + c / 2 / sqrt(B1)
PI_{exakt}: "[" + PI_{links} + "; " + PI_{rechts} + "]"
PI_{Naeherung}: "[" + PI_{NaeherungL} + "; " + PI_{NaeherungR} + "]"
WILSON: "[" + WILSON_{links} + "; " + WILSON_{rechts} + "]"
Text2: "Niveau: " + (round((a * 100), 2)) + " %"
Text3: "f_+(p)=p+" + (LaTeX[c]) + "\frac{\sqrt{p(1-p)}}{\sqrt{n}"
Text4: "f_-(p)=p- " + (LaTeX[c]) + "\frac{\sqrt{p(1-p)}}{\sqrt{n}"
b = true
C5: "" + PI_{exakt} + ""
C10: "" + WILSON + ""
C11: "" + WALD + ""
Eingabefeld1 = Textfield(B7)
D11: WALD_{rechts} - WALD_{links}
D10: WILSON_{rechts} - WILSON_{links}
D5: PI_{rechts} - PI_{links}
Eingabefeld2 = Textfield(B2)
Text6: "Prognoseintervall: " + C5 + "
Länge: " + D5 + "
Konfidenzintervall: " + C10 + "
Länge:" + D10 + "
Konfidenzintervall Näherung: " + C11 + "
Länge: " + D11 + ""