Beispiel: Konfidenzintervall für den Mittelwert

Funktionen > Statistik > Beschreibende Statistik > Beispiel: Konfidenzintervall für den Mittelwert

Berechnen Sie ein Konfidenzintervall für eine Schätzung des Mittelwertes einer normalen Grundgesamtheit, wenn die Varianz der Grundgesamtheit nicht bekannt ist.

1. Definieren Sie einen Stichproben-Datensatz.

2. Verwenden Sie die Funktionen length, mean und stdev, um die Stichprobenstatistiken zu sammeln.

Anzahl der Stichproben	<region id="ID0E3MQAB" top="921.60000000000014" left="288.00000000000006" height="25.6" width="125.05666666666667" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="87"> <define xmlns="http://schemas.mathsoft.com/math50"> <id labels="*" xml:space="preserve">N</id> <apply> <id labels="FUNCTION" xml:space="preserve" label-is-contextual="true">length</id> <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">data</id> </apply> </define> <resultFormat> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" /> </resultFormat> </math> </region>	<region id="ID0EQNQAB" top="921.60000000000014" left="499.20000000000005" height="25.6" width="60.573333333333338" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="89"> <eval xmlns="http://schemas.mathsoft.com/math50"> <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">N</id> <unitOverride> <placeholder /> </unitOverride> </eval> <resultFormat> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" /> </resultFormat> </math> </region>
Mittelwert der Stichprobe	<region id="ID0ETOQAB" top="960.00000000000011" left="288.00000000000006" height="27.791200000000003" width="125.12333333333334" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="91"> <define xmlns="http://schemas.mathsoft.com/math50"> <id labels="*" xml:space="preserve"> <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">m<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">s</Subscript></Span> </id> <apply> <id labels="FUNCTION" xml:space="preserve" label-is-contextual="true">mean</id> <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">data</id> </apply> </define> <resultFormat> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" /> </resultFormat> </math> </region>	<region id="ID0EHPQAB" top="960.00000000000011" left="499.20000000000005" height="27.791200000000003" width="86.673333333333346" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="93"> <eval xmlns="http://schemas.mathsoft.com/math50"> <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true"> <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">m<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">s</Subscript></Span> </id> <unitOverride> <placeholder /> </unitOverride> </eval> <resultFormat> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" /> </resultFormat> </math> </region>
Standardabweichung der Stichprobe	<region id="ID0EKQQAB" top="1017.6000000000001" left="288.00000000000006" height="50.065333527326587" width="176.1426666369041" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="95"> <define xmlns="http://schemas.mathsoft.com/math50"> <id labels="*" xml:space="preserve">s</id> <apply> <mult /> <apply> <id labels="FUNCTION" xml:space="preserve" label-is-contextual="true">stdev</id> <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">data</id> </apply> <apply> <nthRoot /> <placeholder /> <apply> <div /> <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">N</id> <apply> <minus /> <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">N</id> <real>1</real> </apply> </apply> </apply> </apply> </define> <resultFormat> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" /> </resultFormat> </math> </region>	<region id="ID0E5QQAB" top="1017.6000000000001" left="499.20000000000005" height="25.6" width="74.916666666666671" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="97"> <eval xmlns="http://schemas.mathsoft.com/math50"> <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">s</id> <unitOverride> <placeholder /> </unitOverride> </eval> <resultFormat> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" /> </resultFormat> </math> </region>
Freiheitsgrade	<region id="ID0EBSQAB" top="1075.2000000000003" left="288.00000000000006" height="25.6" width="68.183333333333337" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="99"> <define xmlns="http://schemas.mathsoft.com/math50"> <id labels="*" xml:space="preserve">ν</id> <apply> <minus /> <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">N</id> <real>1</real> </apply> </define> <resultFormat> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" /> </resultFormat> </math> </region>	<region id="ID0EVSQAB" top="1075.2000000000003" left="499.20000000000005" height="25.6" width="56.493333333333339" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="101"> <eval xmlns="http://schemas.mathsoft.com/math50"> <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">ν</id> <unitOverride> <placeholder /> </unitOverride> </eval> <resultFormat> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" /> </resultFormat> </math> </region>

3. Geben Sie das zweiseitige Signifikanzniveau ein.

Dies entspricht einem Konfidenzintervall von 95 %.

4. Verwenden Sie die Funktion qt, um das 95. Perzentil der Student-t-Verteilung für einen zweiseitigen Test zu berechnen.

5. Berechnen Sie den oberen und unteren Grenzwert des Konfidenzintervalls.

6. Plotten Sie die Beispieldaten, ihren Mittelwert und das Konfidenzintervall.

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7. Verwenden Sie die Funktion pt, um die kumulative Wahrscheinlichkeitsverteilung für das Konfidenzintervall zu berechnen:

8. Verwenden Sie die Funktion rt, um einen Vektor von Zufallszahlen zu erstellen, die eine Student-t-Verteilung aufweisen:

Das Neuberechnen des Arbeitsblatts bewirkt, dass die Funktion rt einen anderen Satz von Zufallszahlen zurückgibt.

Zugehörige Themen

Mittelwertfunktionen

Student-t-Verteilung

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