Bài giảng xác suất thống kê và ứng dụng phần 10 phan thanh hồng

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Bài giảng xác suất thống kê và ứng dụng phần 10   phan thanh hồng

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❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ P❤❛♥ ỗ ổ t P ỗ ❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✾ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✶ ✴ ✺✶ P❤➛♥ ❳ P t ữỡ s P ỗ ❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✾ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✷ ✴ ✺✶ P❤➛♥ ❳ ✶ ❑❤→✐ ♥✐➺♠ ✈➲ ♣❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ ✭❆◆❖❱❆✮ ✷ P❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ ♠ët ②➳✉ tè ✭♦♥❡✲✇❛② ❆◆❖❱❆✮ ✸ P❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ ❤❛✐ ②➳✉ tè ✭t✇♦✲✇❛② ❆◆❖❱❆✮ ✹ P t s P ỗ ❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✾ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✸ ✴ ✺✶ P❤➛♥ ❳ ✶ ❑❤→✐ ♥✐➺♠ ✈➲ ♣❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ ✭❆◆❖❱❆✮ ✷ P❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ ♠ët ②➳✉ tè ✭♦♥❡✲✇❛② ❆◆❖❱❆✮ ✸ P❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ ❤❛✐ ②➳✉ tè ✭t✇♦✲✇❛② ❆◆❖❱❆✮ ✹ P t s P ỗ ❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✾ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✸ ✴ ✺✶ P❤➛♥ ❳ ✶ ❑❤→✐ ♥✐➺♠ ✈➲ ♣❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ ✭❆◆❖❱❆✮ ✷ P❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ ♠ët ②➳✉ tè ✭♦♥❡✲✇❛② ❆◆❖❱❆✮ ✸ P❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ ❤❛✐ ②➳✉ tè ✭t✇♦✲✇❛② ❆◆❖❱❆✮ ✹ P t s P ỗ ❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✾ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✸ ✴ ✺✶ P❤➛♥ ❳ ✶ ❑❤→✐ ♥✐➺♠ ✈➲ ♣❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ ✭❆◆❖❱❆✮ ✷ P❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ ♠ët ②➳✉ tè ✭♦♥❡✲✇❛② ❆◆❖❱❆✮ ✸ P❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ ❤❛✐ ②➳✉ tè ✭t✇♦✲✇❛② ❆◆❖❱❆✮ ✹ P t s P ỗ ❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✾ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✸ ✴ ✺✶ ❑❤→✐ ♥✐➺♠ ✈➲ ♣❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ ✭❆◆❖❱❆✮ ●✐↔ sû t❛ ♠✉è♥ ♥❣❤✐➯♥ ❝ù✉ ↔♥❤ ❤÷ð♥❣ ❝õ❛ ♠ët sè ❜✐➳♥ ♥❣✉②➯♥ ♥❤➙♥ ✭❞↕♥❣ ❜✐➳♥ ✤à♥❤ t➼♥❤✮ ❧➯♥ ♠ët ❜✐➳♥ ❦➳t q✉↔ ✭❞↕♥❣ ❜✐➳♥ ✤à♥❤ ❧÷đ♥❣✮✳ ✣➸ ❧➔♠ ✤✐➲✉ ✤â ♥❣÷í✐ t❛ t✐➳♥ ❤➔♥❤ s♦ s→♥❤ tr✉♥❣ ❜➻♥❤ ❝õ❛ ♥❤✐➲✉ ♥❤â♠✱ ❝→❝ ♥❤â♠ ♥➔② ❧➔ tê♥❣ t❤➸ ❝→❝ ❣✐→ trà ❝â t❤➸ ❝â ❝õ❛ ❜✐➳♥ ❦➳t q✉↔ ❦❤✐ ❝â sü t→❝ ✤ë♥❣ ❝õ❛ tứ P ỗ ✭✣❍❉▲ ❚❍❿◆● ▲❖◆●✮ ❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✾ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✹ ✴ ✺✶ ❑❤→✐ ♥✐➺♠ ✈➲ ♣❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ ✭❆◆❖❱❆✮ ❈❤➥♥❣ ❤↕♥✱ ✤➸ ♥❣❤✐➯♥ ❝ù✉ ↔♥❤ ❤÷ð♥❣ ❝õ❛ t❤í✐ ❣✐❛♥ tü ❤å❝ tỵ✐ ❦➳t q✉↔ ❤å❝ t➟♣ ❝õ❛ s✐♥❤ ✈✐➯♥✱ ♥➳✉ tớ tỹ ữủ t t ữợ t ữợ t t tr t t q t ủ t t ữợ ỳ ữủ tr✉♥❣ ❜➻♥❤✮ t❤➻ t❛ s➩ ❞ị♥❣ ♣❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ ✤➸ s♦ s→♥❤ ✤✐➸♠ tr✉♥❣ ❜➻♥❤ ❝õ❛ ✸ ♥❤â♠ s✐♥❤ ự ợ trữớ ủ tớ tỹ ❦➸ tr➯♥✳ ❇✐➳♥ ♥❣✉②➯♥ ♥❤➙♥ ð ✤➙② ❧➔ t❤í✐ ❣✐❛♥ tü ❤å❝✱ ❜✐➳♥ ❦➳t q✉↔ ❧➔ ✤✐➸♠ tr✉♥❣ ❜➻♥❤✳ ❚❤æ♥❣ q✉❛ ✈✐➺❝ ❦✐➸♠ ✤à♥❤ t❛ s➩ ❦➳t ❧✉➟♥ t❤í✐ ❣✐❛♥ tỹ õ ữ tợ t q t ❤❛② ❦❤ỉ♥❣✳ ◆➳✉ ❝❤➾ r❛ ✤÷đ❝ ✤✐➸♠ tr✉♥❣ ❜➻♥❤ ❝õ❛ ✸ ♥❤â♠ s✐♥❤ ✈✐➯♥ ❦❤æ♥❣ ❦❤→❝ ♥❤❛✉ t❛ ❦➳t ❧✉➟♥ tố tớ tỹ ổ ữ tợ ❦➳t q✉↔ ❤å❝ t➟♣ ❝õ❛ ❝→❝ s✐♥❤ ✈✐➯♥ ✈➔ ♥❣÷đ❝ P ỗ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✾ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✺ ✴ ✺✶ ❑❤→✐ ♥✐➺♠ ✈➲ ♣❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ ✭❆◆❖❱❆✮ ❈❤➥♥❣ ❤↕♥✱ ✤➸ ♥❣❤✐➯♥ ❝ù✉ ↔♥❤ ❤÷ð♥❣ ❝õ❛ t❤í✐ ❣✐❛♥ tü ❤å❝ tỵ✐ ❦➳t q✉↔ ❤å❝ t➟♣ ❝õ❛ s✐♥❤ ✈✐➯♥✱ ♥➳✉ t❤í✐ ❣✐❛♥ tü ❤å❝ ✤÷đ❝ t❤✉ t ữợ t ữợ t t tr t t q t ủ t t ữợ ❞ú ❧✐➺✉ ✤à♥❤ ❧÷đ♥❣✭✤✐➸♠ tr✉♥❣ ❜➻♥❤✮ t❤➻ t❛ s➩ ❞ị♥❣ ♣❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ ✤➸ s♦ s→♥❤ ✤✐➸♠ tr✉♥❣ ❜➻♥❤ õ s ự ợ trữớ ủ t❤í✐ ❣✐❛♥ tü ❤å❝ ❦➸ tr➯♥✳ ❇✐➳♥ ♥❣✉②➯♥ ♥❤➙♥ ð ✤➙② ❧➔ t❤í✐ ❣✐❛♥ tü ❤å❝✱ ❜✐➳♥ ❦➳t q✉↔ ❧➔ ✤✐➸♠ tr✉♥❣ ❜➻♥❤✳ ❚❤æ♥❣ q✉❛ ✈✐➺❝ ❦✐➸♠ ✤à♥❤ t❛ s➩ t tớ tỹ õ ữ tợ ❦➳t q✉↔ ❤å❝ t➟♣ ❤❛② ❦❤ỉ♥❣✳ ◆➳✉ ❝❤➾ r❛ ✤÷đ❝ ✤✐➸♠ tr✉♥❣ ❜➻♥❤ ❝õ❛ ✸ ♥❤â♠ s✐♥❤ ✈✐➯♥ ❦❤æ♥❣ ❦❤→❝ ♥❤❛✉ t❛ ❦➳t ❧✉➟♥ ②➳✉ tè t❤í✐ ❣✐❛♥ tü ❤å❝ ổ ữ tợ t q t s ữủ P ỗ ▲❖◆●✮ ❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✾ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✺ ✴ ✺✶ 50 24 55 60 26 65 28 70 30 75 80 32 ❑❤→✐ ♥✐➺♠ ✈➲ ♣❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ ✭❆◆❖❱❆✮ A B C Bottom P ỗ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ Middle Top ◆❣➔② ✾ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✻ ✴ ✺✶ ❱➼ ữợ ữỡ s ✷ ✸ ✹ P❤÷ì♥❣ P❤÷ì♥❣ P❤÷ì♥❣ P❤÷ì♥❣ s❛✐ s❛✐ s❛✐ s❛✐ ❣✐ú❛ ❝→❝ ♥❤â♠ ▼❙● = ✶✶✸✻.✾✹ ❣✐ú❛ ❝→❝ ❦❤è✐ ▼❙❇ = ✽.✽✷ ❣✐ú❛ ❝→❝ æ ▼❙■ = ✺.✵✹ ♣❤➛♥ ữ = . P ỗ ❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✾ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✹✶ ✴ ✺✶ ❱➼ ❞ö ữợ tt ự þ ♥❣❤➽❛ α = ✵.✵✺ ❚➼♥❤ t✛ sè ❋✶ = ✵.✽✷✸ ❋✷ = ✶✽✺.✻✷✸, ✶ ❋✸ = ✶.✹✹ ✈➔ ❋(❦ −✶)(❤−✶),❦❤(♠−✶),α = ❋✷,✶✷,✵.✵✺ = ✸.✽✾ ❧ỵ♥ ❤ì♥ ❋✸ ♥➯♥ ❦❤ỉ♥❣ ❜→❝ ❜ä ❣✐↔ t❤✉②➳t ❍✵ ✿ ❑❤ỉ♥❣ ❝â ↔♥❤ ❤÷ð♥❣ t÷ì♥❣ t→❝ ❣✐ú❛ ②➳✉ tè t❤ù ♥❤➜t ✈➔ ②➳✉ tè t❤ù ❤❛✐ ✭❍✵ tr♦♥❣ tr÷í♥❣ ❤đ♣ ♥➔② ❝â ♥❣❤➽❛ ❧➔✿ ↔♥❤ ❤÷ð♥❣ ❝õ❛ ❝❤✐➲✉ ❝❛♦ ❣✐→ ✤ü♥❣ ❤➔♥❣ ❧➯♥ sè s rt ữ ố ợ ✤ë rë♥❣ ❦❤→❝ ♥❤❛✉ ✈➔ ♥❣÷đ❝ ❧↕✐✮ ✷ ❋❦ −✶,❦❤(♠−✶),α = ❋✷,✶✷,✵.✵✺ = ✸.✽✾ ♥❤ä ❤ì♥ ❋✷ ♥➯♥ ❜→❝ ❜ä ❣✐↔ t❤✉②➳t ❍✵ ✿ ❚r✉♥❣ ❜➻♥❤ ❦ tê♥❣ t❤➸ t❤❡♦ ②➳✉ tè ♥❣✉②➯♥ ♥❤➙♥ t❤ù ♥❤➜t ❧➔ ❜➡♥❣ ♥❤❛✉ P❤❛♥ ỗ st ố ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✾ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✹✷ ✴ ✺✶ 80 70 65 60 50 55 Doanh so trung binh 70 65 60 55 75 50 Doanh so trung binh 75 80 ❱➼ ❞ö ✸ DoRong P ỗ ❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ChieuCao ◆❣➔② ✾ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✹✸ ✴ ✺✶ ❱➼ ❞ö ✸ ✸ ❋❤−✶,❦❤(♠−✶),α = ❋✶,✶✷,✵.✵✺ = ✹.✼✺ ❧ỵ♥ ❤ì♥ ❋✸ ♥➯♥ ❦❤ỉ♥❣ ❜→❝ ❜ä ❣✐↔ t❤✉②➳t ❍✵ ✿ ❚r✉♥❣ ❜➻♥❤ ❦ tê♥❣ t❤➸ t❤❡♦ ②➳✉ tè ♥❣✉②➯♥ tự P ỗ ❚❍❿◆● ▲❖◆●✮ ❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✾ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✹✹ ✴ ✺✶ P❤➙♥ t➼❝❤ s➙✉ ❆◆❖❱❆✲tr÷í♥❣ ❤đ♣ ♠ët ②➳✉ tè ▼ư❝ ✤➼❝❤ ❝õ❛ ♣❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ ❧➔ ❦✐➸♠ ✤à♥❤ ❣✐↔ t❤✉②➳t ❍ ✵ : µ✶ = µ ✷ = · · à = tt ố : ỗ t↕✐ ➼t ♥❤➜t ❤❛✐ tr♦♥❣ sè µ✶ , µ✷ , , µ❦ ❦❤→❝ ♥❤❛✉ ◆➳✉ s❛✉ ❦❤✐ ♣❤➙♥ t➼❝❤ t❛ ❜→❝ ❜ä ❍✵ ✱ t❤➻ s❛✉ ✤â t❛ t✐➳♥ ❤➔♥❤ ♣❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ s➙✉ ❤ì♥ ✤➸ s♦ s→♥❤ ❝→❝ tr✉♥❣ ❜➻♥❤ ❝õ❛ ❝→❝ tê♥❣ t❤➸✳ ❱ỵ✐ ❦ tê♥❣ t❤➸ t❛ ♣❤↔✐ t✐➳♥ ❤➔♥❤ s♦ s→♥❤ ❈❦✷ ❝➦♣ tr✉♥❣ ❜➻♥❤✳ ❈❤➥♥❣ ❤↕♥ ✈ỵ✐ ❦ = ✸✱ ❝→❝ ❣✐↔ t❤✉②➳t ❝➛♥ ❦✐➸♠ ✤à♥❤ ❧➔ ❍✵ : µ✶ = µ✷ ❍✶ : µ✶ = µ✷ ❍✵ : µ✶ = µ✸ ❍ ✶ : µ✶ = µ✸ ❍✵ : µ✷ = µ✸ ❍✶ : µ✷ = µ✸ ❚❛ s➩ ❦✐➸♠ ✤à♥❤ ❝→❝ ❣✐↔ t❤✉②➳t tr➯♥ ❜➡♥❣ ♣❤÷ì♥❣ ♣❤→♣ ❚✉❦❡② ♥❤÷ s P ỗ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✾ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✹✺ ✴ ✺✶ P❤➙♥ t➼❝❤ s➙✉ ❆◆❖❱❆✲P❤÷ì♥❣ ♣❤→♣ ❚✉❦❡② ❚➼♥❤ ❣✐→ trà tỵ✐ ❤↕♥ ❚✉❦❡② ❚ = qα,❦ ,♥−❦ ▼❙❲ ♥ ❚r♦♥❣ ✤â qα,❦ ,♥−❦ ①→❝ ✤à♥❤ ❜ð✐ P (❳ > qα,❦ ,♥−❦ ) = α tr♦♥❣ ✤â ❳ ♣❤➙♥ ♣❤è✐ ❚✉❦❡② ✈ỵ✐ ❜➟❝ tü ❞♦ ❦ ✈➔ ♥ − ❦ ✱ ✭♥ = ♥✶ + ♥✷ + · · · + ♥❦ ✮ ▼❙❲ ❧➔ ♣❤÷ì♥❣ s❛✐ tr♦♥❣ ♥ë✐ ❜ë ♥❤â♠ ♥ ❧➔ sè q✉❛♥ s→t tr♦♥❣ ♠é✐ ♥❤â♠✱ ♥➳✉ ❝→❝ ♥✐ ❦❤→❝ ♥❤❛✉ t❤➻ ♥ ❧➔ sè ♥✐ ♥❤ä ♥❤➜t ◆➳✉ |①✐ − ①❥ | > ❚ t❤➻ t❛ ❝❤➜♣ ♥❤➟♥ ❣✐↔ t❤✉②➳t µ✐ ✱ µ❥ = P ỗ ❚❍❿◆● ▲❖◆●✮ ❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✾ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✹✻ ✴ ✺✶ P❤➙♥ t➼❝❤ s➙✉ ❆◆❖❱❆✲P❤÷ì♥❣ ♣❤→♣ ❚✉❦❡② ❚r♦♥❣ ✈➼ ❞ư ✷✱ t❛ ❝â ①✶ = ✺✺.✽✱ ①✷ = ✼✼.✷✱①✸ = ✺✶.✺✱ ▼❙❲ = ✻.✶✻✱ ❧➜② α = ✵.✵✺ ❚ = qα,❦ ,♥−❦ ▼❙❲ ♥ ① = ✻✶.✺ = q✵.✵✺,✸,✶✺ ✻.✶✻ = ✸.✻✼ × ✶.✵✶✸ = ✸.✼✷✷ ✻ ❉♦ |①✶ − ①✷ | = |✺✺.✽ − ✼✼.✷| = ✷✶.✹ > ❚ ♥➯♥ ❝❤➜♣ ♥❤➟♥ ❣✐↔ t❤✉②➳t µ✶ ✱ µ✷ ❦❤→❝ ♥❤❛✉ |①✶ − ①✸ | = |✺✺.✽ − ✺✶.✺| = ✹.✸ > ❚ ♥➯♥ ❝❤➜♣ ♥❤➟♥ ❣✐↔ t❤✉②➳t µ✶ ✱ µ✸ ❦❤→❝ ♥❤❛✉ |①✷ − ①✸ | = |✼✼.✷ − ✺✶.✺| = ✷✺.✼ > ❚ ♥➯♥ ❝❤➜♣ ♥❤➟♥ ❣✐↔ t❤✉②➳t µ✷ ✱ µ✸ ❦❤→❝ ♥❤❛✉ ❱➔ ❞♦ ①✸ < ①✶ < ①✷ < < tự số ữủ s↔♥ ♣❤➞♠ ❜→♥ ✤÷đ❝ tr✉♥❣ ❜➻♥❤ ♥❤✐➲✉ ♥❤➜t ð ♥❣➠♥ ỳ rỗ ữợ t t tr ũ P ỗ ❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✾ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✹✼ ✴ ✺✶ P❤➙♥ t➼❝❤ s➙✉ ❆◆❖❱❆✲tr÷í♥❣ ❤đ♣ ❤❛✐ ②➳✉ tè ❚r÷í♥❣ ❤đ♣ ♣❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ ❤❛✐ ②➳✉ tè✱ ❦❤✐ ❦➳t ❧✉➟♥ ❝â sü ❦❤→❝ ♥❤❛✉ ❣✐ú❛ tr✉♥❣ ❜➻♥❤ ❝õ❛ ❝→❝ ♥❤â♠ ✭❦❤è✐✮ t❛ t✐➳♥ ❤➔♥❤ ♣❤➙♥ t➼❝❤ s➙✉ ✤➸ s♦ s→♥❤ ❝→❝ tr✉♥❣ ❜➻♥❤ tr♦♥❣ ♥❤â♠ ✭❦❤è✐✮ ✈ỵ✐ ♥❤❛✉✳ ✣➸ s♦ s→♥❤ t❤❡♦ ②➳✉ tè t❤ù ♥❤➜t✱ ❣✐→ trà tỵ✐ ❤↕♥ ❚✶ = qα,❦ ,❦❤(♠−✶) ▼❙❊ ❤×♠ ✣➸ s♦ s→♥❤ t❤❡♦ ②➳✉ tè t❤ù ❤❛✐✱ ❣✐→ trà tỵ✐ ❤↕♥ ❚✷ = qα,❤,❦❤(♠−✶) ▼❙❊ ì P ỗ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✾ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✹✽ ✴ ✺✶ P❤➙♥ t➼❝❤ s➙✉ ❆◆❖❱❆✲P❤÷ì♥❣ ♣❤→♣ ❚✉❦❡② ◆➳✉ |①✐ − ①❥ | > ❚✶ t❤➻ ❝❤➜♣ ♥❤➟♥ ❣✐↔ t❤✉②➳t tr✉♥❣ ❜➻♥❤ tê♥❣ t❤➸ ❝õ❛ ♥❤â♠ ✐ ✈➔ ❥ ❦❤→❝ ♥❤❛✉✳ ◆➳✉ |① ✐ − ① ❥ | > ❚✶ t❤➻ ❝❤➜♣ ♥❤➟♥ ❣✐↔ t❤✉②➳t tr✉♥❣ ❜➻♥❤ tê♥❣ t❤➸ ❝õ❛ ❦❤è✐ ✐ ✈➔ ❥ ❦❤→❝ ♥❤❛✉✳ P ỗ st ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✾ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✹✾ ✴ ✺✶ P❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ tr♦♥❣ ❘ ❛♥♦✈❛✭♦❜❥❡❝t✱✳✳✳✮ ❚✉❦❡②❍❙❉ ✭①✱✳✳✳✮ P❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ P❤➙♥ t➼❝❤ s➙✉ ữỡ P ỗ ❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✾ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✺✵ ✴ ✺✶ P❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ tr♦♥❣ ❘✲❱➼ ❞ư ✷ ❚❛ ❝â t❤➸ t✐➳♥ ❤➔♥❤ ❦✐➸♠ ✤à♥❤ ✈➲ sü ❜➡♥❣ ♥❤❛✉ ❝õ❛ ❝→❝ tr✉♥❣ ❜➻♥❤ tr♦♥❣ ✈➼ ❞ư ✷ tr➯♥ ✤➙② tr♦♥❣ ❘ ♥❤÷ s❛✉ ❃ ❃ ❃ ❃ ❉♦❛♥❤❙♦ ❂ ❝✭✺✽✳✷✱ ✺✸✳✼✱ ✺✺✳✽✱ ✳✳✳✮ ◆❤♦♠ ❂ ❣❧✭✸✱✻✮ P❤❛♥❚✐❝❤ ❂ ❧♠✭❉♦❛♥❤❙♦ ∼ ◆❤♦♠✮ ❛♥♦✈❛ ✭P❤❛♥❚✐❝❤✮ # ♥❤➟♣ ❞ú ❧✐➺✉ ❆♥❛❧②s✐s ♦❢ ❱❛r✐❛♥❝❡ ❚❛❜❧❡ ❘❡s♣♦♥s❡✿ ❉♦❛♥❤❙♦ ◆❤♦♠ ❘❡s✐❞✉❛❧s ❉❢ ✷ ✶✺ ❙✉♠ ❙q ✷✷✼✸✳✽✽ ✾✷✳✹✵ q P ỗ ✭✣❍❉▲ ❚❍❿◆● ▲❖◆●✮ ❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ Pr (> ❋ ) ✷✳✼✸✻❡✲✶✶ ◆❣➔② ✾ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✺✶ ✴ ✺✶ P❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ tr♦♥❣ ❘✲❱➼ ❞ö ✷ ❚❛ ❝â t❤➸ t✐➳♥ ❤➔♥❤ ❦✐➸♠ ✤à♥❤ ✈➲ sü ❜➡♥❣ ♥❤❛✉ ❝õ❛ ❝→❝ tr✉♥❣ ❜➻♥❤ tr♦♥❣ ✈➼ ❞ư ✷ tr➯♥ ✤➙② tr♦♥❣ ❘ ♥❤÷ s❛✉ ❃ ❃ ❃ ❃ ❉♦❛♥❤❙♦ ❂ ❝✭✺✽✳✷✱ ✺✸✳✼✱ ✺✺✳✽✱ ✳✳✳✮ ◆❤♦♠ ❂ ❣❧✭✸✱✻✮ P❤❛♥❚✐❝❤ ❂ ❧♠✭❉♦❛♥❤❙♦ ∼ ◆❤♦♠✮ ❛♥♦✈❛ ✭P❤❛♥❚✐❝❤✮ # ♥❤➟♣ ❞ú ❧✐➺✉ ❆♥❛❧②s✐s ♦❢ ❱❛r✐❛♥❝❡ ❚❛❜❧❡ ❘❡s♣♦♥s❡✿ ❉♦❛♥❤❙♦ ◆❤♦♠ ❘❡s✐❞✉❛❧s ❉❢ ✷ ✶✺ ❙✉♠ ❙q ✷✷✼✸✳✽✽ ✾✷✳✹✵ ▼❡❛♥ ❙q P ỗ ▲❖◆●✮ ❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ Pr (> ❋ ) ✷✳✼✸✻❡✲✶✶ ◆❣➔② ✾ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✺✶ ✴ ✺✶ P❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ tr♦♥❣ ❘✲❱➼ ❞ö ✷ ❚❛ ❝â t❤➸ t✐➳♥ ❤➔♥❤ ❦✐➸♠ ✤à♥❤ ✈➲ sü ❜➡♥❣ ♥❤❛✉ ❝õ❛ ❝→❝ tr✉♥❣ ❜➻♥❤ tr♦♥❣ ✈➼ ❞ö ✷ tr➯♥ ✤➙② tr♦♥❣ ❘ ♥❤÷ s❛✉ ❃ ❃ ❃ ❃ ❉♦❛♥❤❙♦ ❂ ❝✭✺✽✳✷✱ ✺✸✳✼✱ ✺✺✳✽✱ ✳✳✳✮ ◆❤♦♠ ❂ ❣❧✭✸✱✻✮ P❤❛♥❚✐❝❤ ❂ ❧♠✭❉♦❛♥❤❙♦ ∼ ◆❤♦♠✮ ❛♥♦✈❛ ✭P❤❛♥❚✐❝❤✮ # ♥❤➟♣ ❞ú ❧✐➺✉ ❆♥❛❧②s✐s ♦❢ ❱❛r✐❛♥❝❡ ❚❛❜❧❡ ❘❡s♣♦♥s❡✿ ❉♦❛♥❤❙♦ ◆❤♦♠ ❘❡s✐❞✉❛❧s ❉❢ ✷ ✶✺ ❙✉♠ ❙q ✷✷✼✸✳✽✽ ✾✷✳✹✵ ▼❡❛♥ ❙q ✶✶✸✻✳✾✹ ✻✳✶✻ P ỗ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ Pr (> ❋ ) ✷✳✼✸✻❡✲✶✶ ◆❣➔② ✾ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✺✶ ✴ ✺✶ P❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ tr♦♥❣ ❘✲❱➼ ❞ư ✸ ❃ ❃ ❃ ❃ ❃ ❉♦❛♥❤❙♦ ❂ ❝✭✺✽✳✷✱ ✺✸✳✼✱ ✺✺✳✽✱ ✳✳✳✮ ◆❤♦♠ ❂ ❣❧✭✸✱ ✻✮ ❑❤♦✐ ❂ ❣❧✭✷✱ ✸✱ ❧❡♥❣t❤❂ ✶✽✮ P❤❛♥❚✐❝❤ ❂ ❧♠✭❉♦❛♥❤❙♦ ∼ ◆❤♦♠ ✰ ❑❤♦✐ ✰ ◆❤♦♠ ❑❤♦✐✮ ❛♥♦✈❛ ✭P❤❛♥❚✐❝❤✮ ❆♥❛❧②s✐s ♦❢ ❱❛r✐❛♥❝❡ ❚❛❜❧❡ ❘❡s♣♦♥s❡✿ ❉♦❛♥❤❙♦ ◆❤♦♠ ❑❤♦✐ ◆❤♦♠✿❑❤♦✐ ❘❡s✐❞✉❛❧s ❉❢ ✷ ✶ ✷ ✶✷ ❙✉♠ ❙q ✷✷✼✸✳✽✽ ✽✳✽✷ ✶✵✳✵✽ ✼✸✳✺✵ ▼❡❛♥ ❙q ✶✶✸✻✳✾✹ ✽✳✽✷ ✺✳✵✹ ✻✳✶✸ P ỗ ▲❖◆●✮ ❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ Pr (> ❋ ) ✾✳✹✷✹❡✲✶✵ ✵✳✷✺✸✸ ✵✳✹✻✷✺ ◆❣➔② ✾ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✺✷ ✴ ✺✶ P❤➙♥ t➼❝❤ ♣❤÷ì♥❣ s❛✐ tr♦♥❣ ❘✲❱➼ ❞ö ✸ ❃ ❃ ❃ ❃ ❃ ❉♦❛♥❤❙♦ ❂ ❝✭✺✽✳✷✱ ✺✸✳✼✱ ✺✺✳✽✱ ✳✳✳✮ ◆❤♦♠ ❂ ❣❧✭✸✱ ✻✮ ❑❤♦✐ ❂ ❣❧✭✷✱ ✸✱ ❧❡♥❣t❤❂ ✶✽✮ P❤❛♥❚✐❝❤ ❂ ❧♠✭❉♦❛♥❤❙♦ ∼ ◆❤♦♠ ✰ ❑❤♦✐ ✰ ◆❤♦♠ ❑❤♦✐✮ ❛♥♦✈❛ ✭P❤❛♥❚✐❝❤✮ ❆♥❛❧②s✐s ♦❢ ❱❛r✐❛♥❝❡ ❚❛❜❧❡ ❘❡s♣♦♥s❡✿ ❉♦❛♥❤❙♦ ◆❤♦♠ ❑❤♦✐ ◆❤♦♠✿❑❤♦✐ ❘❡s✐❞✉❛❧s ❉❢ ✷ ✶ ✷ ✶✷ ❙✉♠ ❙q ✷✷✼✸✳✽✽ ✽✳✽✷ ✶✵✳✵✽ ✼✸✳✺✵ ▼❡❛♥ ❙q ✶✶✸✻✳✾✹ ✽✳✽✷ ✺✳✵✹ ✻✳✶✸ ❋ ✈❛❧✉❡ ✶✽✺✳✻✷✷✾ ✶✳✹✹✵✵ ✵✳✽✷✷✾ P❤❛♥ ỗ st ố ❦➯ ✈➔ ù♥❣ ❞ö♥❣ Pr (> ❋ ) ✾✳✹✷✹❡✲✶✵ ✵✳✷✺✸✸ ✵✳✹✻✷✺ ◆❣➔② ✾ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✺✷ ✴ ✺✶

Ngày đăng: 10/02/2022, 18:18

Mục lục

    Phân tích phng sai

    Khái nim v phân tích phng sai (ANOVA)

    Phân tích phng sai mt yu t (one-way ANOVA)

    Phân tích phng sai hai yu t (two-way ANOVA)

    Phân tích sâu ANOVA

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