Te Ariā o ngā Wā Whakawhirinaki: He Utauta Hira i roto i ngā Tatauranga
He maha ngā wā ka pāngia ngā tatauranga e ngā raraunga kāore i oti, e ngā mōhiohio hapa rānei. I roto i ngā ngana ki te whakatau i ngā whakatau mai i aua raraunga, ka tino whai tikanga, ka hira hoki te ariā o ngā wā whakawhirinaki. He taputapu tatauranga te wā whakawhirinaki e whakamahia ana hei whakatau tata i ngā tawhā taupori i runga i ngā raraunga tauira. Ehara i te mea ka whakaratohia e tēnei ariā he whakatau tata kotahi (whakatau tata) engari ka whakaratohia hoki he awhe e whakaponohia ana, me tētahi taumata whakawhirinaki, hei kapi i te tawhā pono.
He Kupu Whakataki ki ngā Wā Whakawhirinaki
Ko te āputa whakawhirinaki he āputa i hangaia mai i ngā raraunga tauira, ā, e whakamahia ana hei whakatau tata i tētahi tawhā taupori me tētahi taumata whakawhirinaki. Hei tauira, i te wā e whakatau tata ana i te teitei toharite o ngā ākonga i roto i tētahi kura, kāore e ranea te whakarato noa i tētahi tau kotahi, hei tauira 150 cm; he pai ake te whakarato i tētahi awhe, hei tauira 147 cm ki te 153 cm, me te taumata whakawhirinaki 95%.
I roto i ngā tuhi tatauranga, ka taea tēnei te tuhi penei:
`\[ \bar{X} \pm Z_{\alpha/2} \times \left(\frac{\sigma}{\sqrt{n}}\right) \]`
Dimana:
– Ko te toharite tauira te \(\bar{X}\),
– Ko te uara matua o te tohatoha z i tētahi taumata whakapono (hei tauira, 1.96 mō te 95%) ko \(Z_{\alpha/2}\)
– Ko te \(\sigma\) te paerewa rerekētanga tauira, ā,
– Ko te rahi o te tauira ko \(n\).
Taumata Whakapono
Ko te taumata whakapono he tūponotanga e whakaatu ana i te tino mōhiotanga kei te hipoki te wā i hangaia e tātou i te tawhā taupori tūturu. Ko ngā taumata whakapono ka whakaatuhia i te nuinga o te wā hei ōrau, pērā i te 90%, 95%, 99% rānei.
Hei tauira, ki te mea tātou he 95% te āputa whakapono, ko te tikanga mēnā ka tangohia e tātou he 100 tauira rerekē, ka hangaia he 100 āputa whakapono mai i aua tauira, e tūmanakohia ana ka kapi i te 95 o aua āputa te tawhā taupori tūturu.
Me pēhea te tatau i ngā wā whakawhirinaki
He maha ngā mahi hei tatau i te āputa whakawhirinaki, inā koa mō te toharite taupori. Anei te tukanga whānui:
1. Tangohia he Tauira: Kohia ngā raraunga mai i te taupori e hiahiatia ana, hei tauira, te teitei o ngā ākonga i roto i te akomanga.
2. Tātaihia te Toharite Tauira: Tātaihia te toharite (toharite) o te tauira.
3. Tātaihia te Paerewa Rerekētanga Tauira: Tātaihia te paerewa rerekētanga o te rahi o te tauira.
4. Whakatauhia te Taumata Whakapono: Tīpakohia te taumata whakapono, hei tauira 95%.
5. Uara Matua: Kimihia te uara matua e rite ana ki te taumata whakapono kua tīpakohia (uara Z).
6. Tātaihia te Tapeke Hapa: Mā te whakamahi i te tātai:
\[
\text{Tawhiti Hapa} = Z_{\alpha/2} \times \left(\frac{\sigma}{\sqrt{n}}\right)
\]
7. Te Hanganga o ngā Wā Whakawhirinakitanga:
\[
\left( \bar{X} – \text{Tāwhiti Hapa}, \bar{X} + \text{Tāwhiti Hapa} \right)
\]
Hei tauira, mēnā ko te teitei toharite o tētahi tauira ākonga he 150 cm, ko te paerewa rerekētanga he 10 cm, ko te rahi o te tauira he 30 ākonga, ā, ko te taumata whakapono he 95% (nō reira ko Z = 1.96), ka taea te tatau i te wā whakapono penei:
1. Tauira Toharite (\(\bar{X}\)) : 150 cm
2. Paerewa Rerekētanga (\(\sigma\)) : 10 cm
3. Rahi Tauira (\(n\)) : 30
4. Uara Matua (\(Z\)) : 1.96 (mō te 95% te māia)
\[
\text{Tawhiti Hapa} = 1.96 \times \left(\frac{10}{\sqrt{30}}\right) = 1.96 \times 1.83 = 3.586
\]
5. Wā Whakawhirinaki:
\[
(150 – 3.586, 150 + 3.586) = (146.414, 153.586)
\]
Nō reira, ko te wā whakawhirinaki 95% mō te teitei toharite o te ākonga kei waenganui i te 146.414 cm me te 153.586 cm.
Ngā tono i roto i ngā mara rerekē
He whānui te whakamahinga o ngā wā whakawhirinaki i roto i ngā momo marautanga pūtaiao me ngā tono mahi.
1. Hauora me te Haumanu: I roto i ngā rangahau haumanu, ka whakamahia ngā wā whakawhirinaki hei whakatau tata i te whai huatanga o tētahi maimoatanga. Hei tauira, he maha ngā wā ka pūrongohia te whai huatanga o te kano kano me ngā wā whakawhirinaki hei whakaatu kāore i puta noa mai ngā hua.
2. Pakihi me te Ōhanga: I roto i ngā rangahau mākete, ka whakamahia ngā wā whakawhirinaki hei whakatau tata i te ōrau o ngā kaihoko e pai ana ki tētahi hua. Waihoki, i roto i te ōhanga, ka taea te whakamahi i ngā wā whakawhirinaki hei whakatau tata i ngā reiti kore mahi, i ngā reiti pikinga utu rānei.
3. Ngā Pūtaiao Pāpori: Ka whakamahia e ngā rangahau whakaaro a te marea ngā wā whakawhirinaki hei whakarato i ngā whakatau tata tika ake mō ngā tirohanga a te taupori mō tētahi take.
Ngā Herenga o te Wā Whakawhirinaki
I a rātou e whakamahi ana, he mea nui kia mōhio he herenga anō ō ngā āputa whakawhirinaki. Kāore e taea e rātou te whakautu tika i te pātai mēnā kei roto te tawhā taupori i te āputa; ka whakaratohia e rātou he whakawhirinakitanga tūponotanga anake. Hei tāpiri, ko ngā hua o ngā āputa whakawhirinaki he tino whakawhirinaki ki te tohatoha raraunga me te rahi o te tauira.
Mena kāore ngā raraunga tauira i te tohatoha noa, i te iti rawa rānei o te rahi o te tauira, tera pea kāore i te tika ngā hua. I tētahi atu taha, ko tētahi herenga noa ko te whakaaro o tēnei ariā kāore he pānga pūnaha i roto i ngā inenga, e kore pea e tūturu i roto i ngā āhuatanga o te ao tūturu.
Whakamutunga
He taputapu tatauranga kaha ngā āputa whakawhirinaki mō te whakatau tata i ngā tawhā taupori i runga i ngā raraunga tauira. Mā te whakarato i te whānuitanga o ngā uara e kapi ana i te tawhā taupori tūturu me te taumata whakawhirinaki, ka taea e ēnei āputa te whakatau whai whakaaro me te tika. Heoi, me mōhio tonu ngā kaiwhakamahi ki ngā whakaaro me ngā herenga kei roto i ēnei tikanga. Nō reira, he mea nui te māramatanga hōhonu ki te tatau me te whakamārama i ngā āputa whakawhirinaki kia whai hua ai te whakamahinga i roto i te rangahau me te mahi o ia rā.
