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10.5: Njia mbili za Idadi ya Watu na Mapungufu ya Kiwango cha Kujulikana

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    179643

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    Ingawa hali hii haiwezekani (kujua upungufu wa kiwango cha idadi ya watu hauwezekani sana), mfano unaofuata unaonyesha kupima nadharia kwa njia za kujitegemea na ukiukaji wa kiwango cha idadi ya watu. Usambazaji wa sampuli kwa tofauti kati ya njia ni ya kawaida kwa mujibu wa theorem ya kikomo ya kati. kutofautiana random ni\(\overline{X_{1}}-\overline{X_{2}}\). Usambazaji wa kawaida una muundo wafuatayo:

    \[\textbf{The standard deviation is:}\nonumber\]

    \[\sqrt{\frac{\left(\sigma_{1}\right)^{2}}{n_{1}}+\frac{\left(\sigma_{2}\right)^{2}}{n_{2}}}\nonumber\]

    \[\textbf{The test statistic (z-score) is:}\nonumber\]

    \[Z_{c}=\frac{\left(\overline{x}_{1}-\overline{x}_{2}\right)-\delta_{0}}{\sqrt{\frac{\left(\sigma_{1}\right)^{2}}{n_{1}}+\frac{\left(\sigma_{2}\right)^{2}}{n_{2}}}}\nonumber\]

    Katika kiwango cha 5% cha umuhimu, kutoka kwa data ya sampuli, hakuna ushahidi wa kutosha wa kuhitimisha kuwa umri wa maana wa maseneta wa Kidemokrasia ni mkubwa kuliko umri wa maana wa maseneta wa Republican.