Bài giảng xác suất thống kê và ứng dụng phần 7 phan thanh hồng

❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ P❤❛♥ ỗ t P ỗ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✽ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✶ ✴ ✸✼ P❤➛♥ ❱■■ ❑❤♦↔♥❣ t✐♥ P ỗ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✽ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✷ ✴ ✸✼ P❤➛♥ ❱■■ ✶ ▼ët sè ❦❤→✐ ♥✐➺♠ ✷ ❑❤♦↔♥❣ t✐♥ ❝➟② ❝❤♦ tr✉♥❣ ❜➻♥❤ tê♥❣ t❤➸ ❑❤♦↔♥❣ t✐♥ ❝➟② ❝❤♦ tr✉♥❣ ❜➻♥❤ tê♥❣ t❤➸✱ ❝ï ♠➝✉ ❧ỵ♥ ❑❤♦↔♥❣ t✐♥ ❝➟② ❝❤♦ tr✉♥❣ ❜➻♥❤ tê♥❣ t❤➸✱ ❝ï ♠➝✉ ♥❤ä ✸ ❑❤♦↔♥❣ t✐♥ ❝➟② ❝❤♦ t✛ ❧➺ tờ t ù P ỗ ✭✣❍❉▲ ❚❍❿◆● ▲❖◆●✮ ❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✽ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✸ ✴ ✸✼ P❤➛♥ ❱■■ ✶ ▼ët sè ❦❤→✐ ♥✐➺♠ ✷ ❑❤♦↔♥❣ t✐♥ ❝➟② ❝❤♦ tr✉♥❣ ❜➻♥❤ tê♥❣ t❤➸ ❑❤♦↔♥❣ t✐♥ ❝➟② ❝❤♦ tr✉♥❣ ❜➻♥❤ tê♥❣ t❤➸✱ ❝ï ♠➝✉ ❧ỵ♥ ❑❤♦↔♥❣ t✐♥ ❝➟② ❝❤♦ tr✉♥❣ ❜➻♥❤ tê♥❣ t❤➸✱ ❝ï ♠➝✉ ♥❤ä ✸ ❑❤♦↔♥❣ t✐♥ ❝➟② ❝❤♦ t✛ ❧➺ tê♥❣ t❤➸ ✹ ❳→❝ ù P ỗ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✽ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✸ ✴ ✸✼ P❤➛♥ ❱■■ ✶ ▼ët sè ❦❤→✐ ♥✐➺♠ ✷ ❑❤♦↔♥❣ t✐♥ ❝➟② ❝❤♦ tr✉♥❣ ❜➻♥❤ tê♥❣ t❤➸ ❑❤♦↔♥❣ t✐♥ ❝➟② ❝❤♦ tr✉♥❣ ❜➻♥❤ tê♥❣ t❤➸✱ ❝ï ♠➝✉ ❧ỵ♥ ❑❤♦↔♥❣ t✐♥ ❝➟② ❝❤♦ tr✉♥❣ ❜➻♥❤ tê♥❣ t❤➸✱ ❝ï ♠➝✉ ♥❤ä ✸ ❑❤♦↔♥❣ t✐♥ ❝➟② ❝❤♦ t✛ ❧➺ tê♥❣ t❤➸ ✹ ❳→❝ ✤à♥❤ ❝ï ♠➝✉ P❤❛♥ ỗ st ố ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✽ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✸ ✴ ✸✼ P❤➛♥ ❱■■ ✶ ▼ët sè ❦❤→✐ ♥✐➺♠ ✷ ❑❤♦↔♥❣ t✐♥ ❝➟② ❝❤♦ tr✉♥❣ ❜➻♥❤ tê♥❣ t❤➸ ❑❤♦↔♥❣ t✐♥ ❝➟② ❝❤♦ tr✉♥❣ ❜➻♥❤ tê♥❣ t❤➸✱ ❝ï ♠➝✉ ❧ỵ♥ ❑❤♦↔♥❣ t✐♥ ❝➟② ❝❤♦ tr✉♥❣ ❜➻♥❤ tê♥❣ t❤➸✱ ❝ï ♠➝✉ ♥❤ä ✸ ❑❤♦↔♥❣ t✐♥ ❝➟② ❝❤♦ t✛ ❧➺ tê♥❣ t❤➸ ù P ỗ ▲❖◆●✮ ❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✽ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✸ ✴ ✸✼ P❤➛♥ ❱■■ ✶ ▼ët sè ❦❤→✐ ♥✐➺♠ ✷ ❑❤♦↔♥❣ t✐♥ ❝➟② ❝❤♦ tr✉♥❣ ❜➻♥❤ tê♥❣ t❤➸ ❑❤♦↔♥❣ t✐♥ ❝➟② ❝❤♦ tr✉♥❣ ❜➻♥❤ tê♥❣ t❤➸✱ ❝ï ♠➝✉ ❧ỵ♥ ❑❤♦↔♥❣ t✐♥ ❝➟② ❝❤♦ tr✉♥❣ ❜➻♥❤ tê♥❣ t❤➸✱ ❝ï ♠➝✉ ♥❤ä ✸ ❑❤♦↔♥❣ t✐♥ ❝➟② ❝❤♦ t✛ ❧➺ tê♥❣ t❤➸ ✹ ❳→❝ ✤à♥❤ ❝ï P ỗ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✽ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✸ ✴ ✸✼ P❤➛♥ ❱■■ ✶ ▼ët sè ❦❤→✐ ♥✐➺♠ ✷ ❑❤♦↔♥❣ t✐♥ ❝➟② ❝❤♦ tr✉♥❣ ❜➻♥❤ tê♥❣ t❤➸ ❑❤♦↔♥❣ t✐♥ ❝➟② ❝❤♦ tr✉♥❣ ❜➻♥❤ tê♥❣ t❤➸✱ ❝ï ♠➝✉ ❧ỵ♥ ❑❤♦↔♥❣ t✐♥ ❝➟② ❝❤♦ tr✉♥❣ ❜➻♥❤ tê♥❣ t❤➸✱ ❝ï ♠➝✉ ♥❤ä ✸ ❑❤♦↔♥❣ t✐♥ ❝➟② ❝❤♦ t✛ ❧➺ tờ t ù P ỗ ✭✣❍❉▲ ❚❍❿◆● ▲❖◆●✮ ❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✽ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✸ ✴ ởt số r ỳ trữợ t tợ ữợ ữủ tr ❜➻♥❤ ♠➝✉ ① ✱ ♣❤÷ì♥❣ s❛✐ ♠➝✉ s ✷ ✱ t ữủt ữợ ữủ tr tờ t ữỡ s tờ t❤➸ σ ✷ ✱ t✛ ❧➺ tê♥❣ t❤➸ ♣ ✳ P s tr ữợ ữủ ♠ët sè t❤❛♠ sè tê♥❣ t❤➸✱ t❤❡♦ ✤â s❛✉ ❦❤✐ t➼♥❤ t♦→♥ tr➯♥ ♠ët ♠➝✉ ❝ö t❤➸ t❛ ❝â t❤➸ t✐♥ r➡♥❣ t❤❛♠ sè tê♥❣ t❤➸ t❤✉ë❝ ✈➔♦ ♠ët ❦❤♦↔♥❣ tr õ P ỗ ❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✽ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✹ ✴ ✸✼ ▼ët sè ❦❤→✐ ♥✐➺♠ ✣à♥❤ ♥❣❤➽❛ ●✐↔ sû θ ❧➔ ♠ët t❤❛♠ số tờ t ữợ ữủ ởt sè ♠➔ ✵ < α < ✶✳ ●✐↔ sû ❞ü❛ tr➯♥ ♠➝✉ ♥❣➝✉ ♥❤✐➯♥ rót tø tê♥❣ t❤➸ t❛ t➻♠ ✤÷đ❝ ❤❛✐ ❜✐➳♥ ♥❣➝✉ ♥❤✐➯♥ ❆ ✈➔ ❇ s❛♦ ❝❤♦ P (❆ ≤ θ ≤ ❇ ) = ✶ − α ❑❤✐ ✤â ❦❤♦↔♥❣ [❆, ❇ ] ✤÷đ❝ ❣å✐ ❧➔ ữợ ữủ t ( )% ợ ởt t ữủ r ❆✱ ❇ ❝â ❣✐→ trà ❛✱❜ t❤➻ ❦❤♦↔♥❣ [❛, ❜] ✤÷đ❝ ❣å✐ ❧➔ ♠ët ❦❤♦↔♥❣ t✐♥ ❝➟② (✶ − α)✶✵✵% ❝❤♦ θ✳ ❙è (✶ − α) ✤÷đ❝ ❣å✐ ❧➔ ✤ë t ữợ ữủ P ỗ ❚❍❿◆● ▲❖◆●✮ ❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✽ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✺ ✴ ✸✼ ❚➻♠ ❦❤♦↔♥❣ t✐♥ ❝➟② ❝❤♦ tr✉♥❣ ❜➻♥❤ tê♥❣ t❤➸ tr♦♥❣ ❘ ❚r÷í♥❣ ❤đ♣ ✸ ◆➳✉ ✶ ♠➝✉ ❞ú ❧✐➺✉ t❤ỉ ❝ï ❧ỵ♥✱ ✷ ❤♦➦❝ tê♥❣ t❤➸ ♣❤➙♥ ♣❤è✐ ❝❤✉➞♥ ✭❦❤ỉ♥❣ ❜✐➳t ✤ë ❧➺❝❤ ❝❤✉➞♥ tê♥❣ t❤➸✮✱ ♠➝✉ ❞ú ❧✐➺✉ t❤æ ❝ï ♥❤ä ❚❛ t➻♠ ❦❤♦↔♥❣ t✐♥ ❝➟② ❝❤♦ tr✉♥❣ ❜➻♥❤ tờ t ữ s ttst r õ ❝♦♥❢✳❧❡✈❡❧✿ ✈❡❝tì ❞ú ❧✐➺✉ ✤ë t✐♥ ❝➟② ✭♠➦❝ ✤à♥❤ ❧➔ . P ỗ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✽ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✷✾ ✴ ✸✼ ❚➻♠ ❦❤♦↔♥❣ t✐♥ ❝➟② ❝❤♦ tr✉♥❣ ❜➻♥❤ tê♥❣ t❤➸ tr♦♥❣ ❘ ❚r÷í♥❣ ❤đ♣ ✸ ◆➳✉ ✶ ♠➝✉ ❞ú ❧✐➺✉ t❤ỉ ❝ï ❧ỵ♥✱ ✷ ❤♦➦❝ tê♥❣ t❤➸ ♣❤➙♥ ♣❤è✐ ❝❤✉➞♥ ✭❦❤æ♥❣ ❜✐➳t ✤ë ❧➺❝❤ ❝❤✉➞♥ tê♥❣ t❤➸✮✱ ♠➝✉ ❞ú ❧✐➺✉ t❤æ ❝ï ♥❤ä ❚❛ t➻♠ ❦❤♦↔♥❣ t tr tờ t ữ s t✳t❡st✭①✱ ❝♦♥❢✳❧❡✈❡❧❂✮ ❚r♦♥❣ ✤â ①✿ ❝♦♥❢✳❧❡✈❡❧✿ ✈❡❝tì ❞ú ❧✐➺✉ ✤ë t . P ỗ ❚❍❿◆● ▲❖◆●✮ ❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✽ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✷✾ ✴ ✸✼ ❚➻♠ ❦❤♦↔♥❣ t✐♥ ❝➟② ❝❤♦ tr✉♥❣ ❜➻♥❤ tê♥❣ t❤➸ tr♦♥❣ rữớ ủ ù ợ t tr✉♥❣ ❜➻♥❤ ♠➝✉ ① ✱ ✤ë ❧➺❝❤ ❝❤✉➞♥ ♠➝✉ s ✷ ❤♦➦❝ tê♥❣ t❤➸ ♣❤➙♥ ♣❤è✐ ❝❤✉➞♥ ✭❦❤æ♥❣ ❜✐➳t ✤ë ❧➺❝❤ ❝❤✉➞♥ tê♥❣ t❤➸✮✱ ❝ï ♠➝✉ ♥❤ä✱ ❜✐➳t tr✉♥❣ ❜➻♥❤ ♠➝✉ ① ✱ ✤ë ❧➺❝❤ ❝❤✉➞♥ ♠➝✉ s ❚❛ t➻♠ t tr tờ t ữ s❛✉✿ ❧✐❜r❛r② ✭❇❙❉❆✮ ts✉♠✳t❡st✭♠❡❛♥✳①✱ s✳①❂ ✱ ♥✳①❂ ✱ ❝♦♥❢✳❧❡✈❡❧❂✮ ❚r♦♥❣ ✤â ♠❡❛♥✳①✿ s✳①✿ ♥✳①✿ ❝♦♥❢✳❧❡✈❡❧✿ tr✉♥❣ ❜➻♥❤ ♠➝✉ ✤ë ❧➺❝❤ ❝❤✉➞♥ ♠➝✉ ❝ï ♠➝✉ ✤ë t✐♥ ❝➟② ✭♠➦❝ ✤à♥❤ ❧➔ . P ỗ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✽ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✸✵ ✴ ✸✼ ❚➻♠ ❦❤♦↔♥❣ t✐♥ ❝➟② ❝❤♦ tr✉♥❣ ❜➻♥❤ tê♥❣ t❤➸ tr♦♥❣ ❘ ❚r÷í♥❣ ❤đ♣ ✹ ◆➳✉ ✶ ❝ï ♠➝✉ ❧ỵ♥✱ ❜✐➳t tr✉♥❣ ❜➻♥❤ ♠➝✉ ① ✱ ✤ë ❧➺❝❤ ❝❤✉➞♥ ♠➝✉ s ✷ ❤♦➦❝ tê♥❣ t❤➸ ♣❤➙♥ ♣❤è✐ ❝❤✉➞♥ ✭❦❤æ♥❣ ❜✐➳t ✤ë ❧➺❝❤ ❝❤✉➞♥ tê♥❣ t❤➸✮✱ ❝ï ♠➝✉ ♥❤ä✱ ❜✐➳t tr✉♥❣ ❜➻♥❤ ♠➝✉ ① ✱ ✤ë ❧➺❝❤ ❝❤✉➞♥ ♠➝✉ s ❚❛ t➻♠ ❦❤♦↔♥❣ t✐♥ ❝➟② ❝❤♦ tr✉♥❣ tờ t ữ s rr tstst s ✱ ♥✳①❂ ✱ ❝♦♥❢✳❧❡✈❡❧❂✮ ❚r♦♥❣ ✤â ♠❡❛♥✳①✿ s✳①✿ ♥✳①✿ ❝♦♥❢✳❧❡✈❡❧✿ tr✉♥❣ ❜➻♥❤ ♠➝✉ ✤ë ❧➺❝❤ ❝❤✉➞♥ ♠➝✉ ❝ï ♠➝✉ ✤ë t . P ỗ ❚❍❿◆● ▲❖◆●✮ ❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✽ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✸✵ ✴ ✸✼ ❚➻♠ ❦❤♦↔♥❣ t✐♥ ❝➟② ❝❤♦ tr✉♥❣ ❜➻♥❤ tê♥❣ t❤➸ tr♦♥❣ rữớ ủ ù ợ t tr✉♥❣ ❜➻♥❤ ♠➝✉ ① ✱ ✤ë ❧➺❝❤ ❝❤✉➞♥ ♠➝✉ s ✷ ❤♦➦❝ tê♥❣ t❤➸ ♣❤➙♥ ♣❤è✐ ❝❤✉➞♥ ✭❦❤æ♥❣ ❜✐➳t ✤ë ❧➺❝❤ ❝❤✉➞♥ tê♥❣ t❤➸✮✱ ❝ï ♠➝✉ ♥❤ä✱ ❜✐➳t tr✉♥❣ ❜➻♥❤ ♠➝✉ ① ✱ ✤ë ❧➺❝❤ ❝❤✉➞♥ ♠➝✉ s ❚❛ t➻♠ t tr tờ t ữ s❛✉✿ ❧✐❜r❛r② ✭❇❙❉❆✮ ts✉♠✳t❡st✭♠❡❛♥✳①✱ s✳①❂ ✱ ♥✳①❂ ✱ ❝♦♥❢✳❧❡✈❡❧❂✮ ❚r♦♥❣ ✤â ♠❡❛♥✳①✿ s✳①✿ ♥✳①✿ ❝♦♥❢✳❧❡✈❡❧✿ tr✉♥❣ ❜➻♥❤ ♠➝✉ ✤ë ❧➺❝❤ ❝❤✉➞♥ ♠➝✉ ❝ï ♠➝✉ ✤ë t✐♥ ❝➟② ✭♠➦❝ ✤à♥❤ ❧➔ . P ỗ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✽ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✸✵ ✴ ✸✼ ❑❤♦↔♥❣ t✐♥ ❝➟② ❝❤♦ t✛ ❧➺ tê♥❣ t❤➸ ˆ ✿ ❦❤✐ ❝ï ♠➝✉ ❚r♦♥❣ ♣❤➛♥ ❱■✱ t❛ ✤➣ ♥❣❤✐➯♥ ❝ù✉ ♣❤➙♥ ♣❤è✐ ❝õ❛ t✛ ❧➺ P ợ P õ ố ữ ố ợ tr = σ ✷ = ♣ (✶ − ♣ )/♥✳ ˆ t❛ ❝â ❩ = ❈❤✉➞♥ ❤â❛ P ˆ −♣ P ✳ ( )/ ữỡ tỹ t ữợ ❧÷đ♥❣ ❦❤♦↔♥❣ ❝❤♦ tr✉♥❣ ❜➻♥❤✱ tø P −③α/✷ ≤ ❩ ≤ ③α/✷ = ✶ − α t❛ ❝â P −③α/✷ ≤ ˆ −♣ P ≤ ③α/✷ = ✶ − α ♣ (✶ − ♣ )/♥ ❚ø ✤â t❛ ❝â ˆ − ③α/✷ P P ˆ + ③α/✷ ♣ (✶ − ♣ )/♥ ≤ ♣ ≤ P ♣ (✶ − ♣ )/ = P ỗ ▲❖◆●✮ ❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✽ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✸✶ ✴ ✸✼ ❑❤♦↔♥❣ t✐♥ ❝➟② ❝❤♦ t✛ ❧➺ tê♥❣ t❤➸ ❉ị ♣ ❦❤ỉ♥❣ t t õ t ũ ữợ ữủ ✤✐➸♠ ❝❤♦ ♣ t❤❛② ✈➔♦ ♣❤÷ì♥❣ tr➻♥❤ tr➯♥ ✤➸ ✤÷đ❝ ❦❤♦↔♥❣ t✐♥ ❝➟② ❝❤♦ ♣ ✳ ❑❤♦↔♥❣ t✐♥ ❝➟② ❝❤♦ ♣ ◆➳✉ ❝ï ♠➝✉ ♥ ❧ỵ♥ ❦❤♦↔♥❣ t✐♥ ❝➟② ❝❤♦ ♣ ❧➔ ♣ˆ − ③α/✷ ♣ˆ(✶ − ♣ˆ)/♥, ♣ˆ + ③α/✷ ♣ˆ(✶ − ♣ˆ)/♥ = ♣ˆ ± ③α/✷ ♣ˆ(✶ − )/ r õ ữủ ợ ˆ ≥ ✺ ✈➔ ♥(✶ − ♣ˆ) ≥ ✺ P❤❛♥ ỗ st ố ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✽ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✸✷ ✴ ✸✼ ❱➼ ❞ö ❱➼ ❞ö✿ ❚❤✉è❝ ❦❤→♥❣ s✐♥❤ ổ r t tr ỗ ♥ỉ♥ ❝❤♦ ♥❣÷í✐ sû ❞ư♥❣ ♥❤÷ ♠ët t→❝ ❞ư♥❣ ♣❤ư✳ ❚↕✐ ♠ët ❝ỉ♥❣ t② ❞÷đ❝✱ ❝→❝ ♥❤➔ ❦❤♦❛ ❤å❝ ✈ø❛ ♣❤→t tr✐➸♥ ♠ët ❧♦↕✐ t❤✉è❝ ❦❤→♥❣ s✐♥❤ ♠ỵ✐ ❝â t➯♥ P ổ t ố ữợ ữủ t ỗ ổ ũ tố ▼ët ♠➝✉ ♥❣➝✉ ♥❤✐➯♥ ✷✵✵ ❜➺♥❤ ♥❤➙♥ ✤÷đ❝ ❝❤å♥ ❝â ỗ ổ t t ❝➟② ✾✺% ❝❤♦ t✛ ❧➺ t➜t ❝→❝ ❝→❝ ❜➺♥❤ ♥❤➙♥ ỗ ổ ũ tố P ỗ ✭✣❍❉▲ ❚❍❿◆● ▲❖◆●✮ ❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✽ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✸✸ ✴ ✸✼ ❱➼ ❞ư ▲í✐ ❣✐↔✐✿ ♥ = ✷✵✵✱ α = . / = . = . ìợ ❧÷đ♥❣ ✤✐➸♠ ❝❤♦ t✛ ❧➺ tê♥❣ t❤➸ ❧➔ ♣ˆ = ✸✺ = ✵.✶✼✺ ✷✵✵ ♥♣ˆ = ✸✺✱ ♥(✶ − ♣ˆ) = ✶✻✺ ✤➲✉ ❧ỵ♥ ❤ì♥ ✺✳ ◆➯♥ ❦❤♦↔♥❣ t✐♥ ❝➟② ✾✺% ❝❤♦ ♣ ❧➔ ✵.✶✼✺.✵.✽✷✺ ♣ˆ ± ③α/✷ ♣ˆ(✶ − ♣ˆ)/♥ = ✵.✶✼✺ ± ✶.✾✻ ✷✵✵ = [✵.✶✼✺ ± ✵.✵✺✸] = [., .] õ P ỗ ❚❍❿◆● ▲❖◆●✮ ❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✽ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✸✹ ✴ ✸✼ ❚➻♠ ❦❤♦↔♥❣ t✐♥ ❝➟② ❝❤♦ t✛ ❧➺ tê♥❣ t❤➸ tr♦♥❣ ❘ ♣r♦♣✳t❡st✭①✱ ♥✱ ❝♦♥❢✳❧❡✈❡❧ ❂ ✱❝♦rr❡❝t ❂ ❋✮ ❤♦➦❝ ❜✐♥♦♠✳t❡st✭①✱ ♥✱ ❝♦♥❢✳❧❡✈❡❧ ❂ ✮ ❚r♦♥❣ ✤â ①✿ ♥✿ ❝♦♥❢✳❧❡✈❡❧✿ sè ♣❤➛♥ tû ❝â t➼♥❤ ❝❤➜t ♥❣❤✐➯♥ ❝ù✉ tr♦♥❣ ♠➝✉ ❝ï ♠➝✉ ✤ë t✐♥ ❝➟② ✭♠➦❝ ✤à♥❤ ❧➔ ✵.✾✺✮ P❤❛♥ ❚❤❛♥❤ ỗ st ố ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✽ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✸✺ ✴ ✸✼ ❚➻♠ ❦❤♦↔♥❣ t✐♥ ❝➟② ❝❤♦ t✛ ❧➺ tê♥❣ t❤➸ tr♦♥❣ ❘ ♣r♦♣✳t❡st✭①✱ ♥✱ ❝♦♥❢✳❧❡✈❡❧ ❂ ✱❝♦rr❡❝t ❂ ❋✮ ❤♦➦❝ ❜✐♥♦♠✳t❡st✭①✱ ♥✱ ❝♦♥❢✳❧❡✈❡❧ ❂ ✮ ❚r♦♥❣ ✤â ①✿ ♥✿ ❝♦♥❢✳❧❡✈❡❧✿ sè ♣❤➛♥ tû ❝â t➼♥❤ ❝❤➜t ♥❣❤✐➯♥ ❝ù✉ tr♦♥❣ ♠➝✉ ❝ï ♠➝✉ ✤ë t✐♥ ❝➟② ✭♠➦❝ ✤à♥❤ ❧➔ ✵.✾✺✮ P ỗ st ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✽ t❤→♥❣ ✾ ♥➠♠ ù ữợ ữủ tr tờ t t t ữợ ữủ ❦❤♦↔♥❣ ❝❤♦ tr✉♥❣ ❜➻♥❤ ❝õ❛ tê♥❣ t❤➸ ♣❤➙♥ ♣❤è✐ ❝❤✉➞♥ ✈ỵ✐ ✤ë ❧➺❝❤ ❝❤✉➞♥ σ ✤➣ ❜✐➳t✳ ❚❛ ❝â ❦❤♦↔♥❣ t✐♥ ❝➟② ✈ỵ✐ ✤ë t✐♥ ❝➟② ✶ − α ❝❤♦ µ ❧➔ σ σ ① − ③α/✷ √ , ① + / ữợ ❧÷đ♥❣ ✤♦ ❜➡♥❣ ❧÷đ♥❣ ✤÷đ❝ ❝ë♥❣ ✈➔♦ ✈➔ trø r❛ ọ tr ợ ữợ tr t ữủ ỵ ❧➔ ❡ ✳ σ ♥ ◆❤÷ ✈➟② ❡ = ③α/✷ ố ữợ ữủ tr ợ trữợ t ổ t❤ù❝ tr➯♥ t❛ ❝â t❤➸ ①→❝ ✤à♥❤ ❝ï ♠➝✉ ♥ ữ s = / P ỗ ✭✣❍❉▲ ❚❍❿◆● ▲❖◆●✮ ❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✽ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✸✻ ✴ ù ữợ ữủ tr tờ t t t ữợ ữủ tr ❜➻♥❤ ❝õ❛ tê♥❣ t❤➸ ♣❤➙♥ ♣❤è✐ ❝❤✉➞♥ ✈ỵ✐ ✤ë ❧➺❝❤ ❝❤✉➞♥ σ ✤➣ ❜✐➳t✳ ❚❛ ❝â ❦❤♦↔♥❣ t✐♥ ❝➟② ✈ỵ✐ ✤ë t✐♥ ❝➟② ✶ − α ❝❤♦ µ ❧➔ σ σ ① − ③α/✷ √ , ① + ③α/✷ √ ữợ ữủ ❧÷đ♥❣ ✤÷đ❝ ❝ë♥❣ ✈➔♦ ✈➔ trø r❛ ❦❤ä✐ tr✉♥❣ ❜➻♥❤ ợ ữợ tr t ữủ ỵ σ ♥ ◆❤÷ ✈➟② ❡ = ③α/✷ √ ✳ ❑❤✐ ố ữợ ữủ tr ợ trữợ t ổ tự tr t ❝â t❤➸ ①→❝ ✤à♥❤ ❝ï ♠➝✉ ♥ ♥❤÷ s❛✉ ♥= / P ỗ ❇➔✐ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✽ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✸✻ ✴ ✸✼ ❳→❝ ✤à♥❤ ù ữợ ữủ tr tờ t t t ữợ ữủ tr tờ t❤➸ ♣❤➙♥ ♣❤è✐ ❝❤✉➞♥ ✈ỵ✐ ✤ë ❧➺❝❤ ❝❤✉➞♥ σ ✤➣ ❜✐➳t✳ ❚❛ ❝â ❦❤♦↔♥❣ t✐♥ ❝➟② ✈ỵ✐ ✤ë t✐♥ ❝➟② ✶ − α ❝❤♦ µ ❧➔ σ σ ① − ③α/✷ √ , ① + ③α/✷ √ ♥ ♥ ✣ë ữợ ữủ ữủ ữủ ✈➔♦ ✈➔ trø r❛ ❦❤ä✐ tr✉♥❣ ❜➻♥❤ ♠➝✉ ❦❤✐ ①→❝ ợ ữợ tr t ữủ ỵ ữ = / ố ữợ ữủ ❝❤♦ tr✉♥❣ ❜➻♥❤ ✈ỵ✐ ✤ë ❝❤➼♥❤ ①→❝ ❡ ✤➣ ①→❝ trữợ t ổ tự tr t õ t ✤à♥❤ ❝ï ♠➝✉ ♥ ♥❤÷ s❛✉ ♥= ③α/✷ σ ✷ P ỗ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✽ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✸✻ ✴ ✸✼ ❳→❝ ✤à♥❤ ❝ï ♠➝✉ ❝❤♦ ÷ỵ❝ t✛ ❧➺ tê♥❣ t❤➸ ❚÷ì♥❣ tü t❛ ❝â ❝ỉ♥❣ tự ù tr t ữợ ữủ ❝❤♦ t✛ ❧➺ tê♥❣ t❤➸ ❦❤✐ ✤ë ❝❤➼♥❤ ①→❝ ❝õ❛ ÷ỵ❝ ❧÷đ♥❣ ❧➔ ❡ ♥= ✷ ♣ (✶ − ♣ ) / r õ õ t ữợ ữủ ỹ ự trữợ õ ♥❣❤✐➺♠ ✤➸ ♣❤ä♥❣ ✤♦→♥✳ ❚❛ ❝ô♥❣ ❝â t❤➸ ❝❤å♥ ❣✐↔✐ ♣❤→♣ ✧❛♥ t♦➔♥✧ ❧➔ ❧➜② ♣ = ✵.✺ P❤❛♥ ❚❤❛♥❤ ỗ st ố ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✽ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✸✼ ✴ ✸✼ ... ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✽ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✶✾ ✴ ✸✼ ▼æ t↔ ♣❤➙♥ ♣❤è✐ t Duong phan phoi chuan hoa Duong phan phoi t voi df=19 Duong phan phoi t voi df=4 P ỗ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✽ t❤→♥❣... ❚❤❛♥❤ ỗ st ố ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✽ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✷✷ ✴ ✸✼ ●✐→ trà t♥,α Duong phan phoi t voi n bac tu Duong phan phoi t voi 14 bac tu α t n, α P❤❛♥ ❚❤❛♥❤ ỗ st ố ✈➔ ù♥❣ ❞ö♥❣ 0.025 t14,... P ỗ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ ◆❣➔② ✽ t❤→♥❣ ✾ ♥➠♠ ✷✵✵✾ ✷✹ ✴ ✸✼ ●✐→ trà t♥−✶,α/✷ Duong phan phoi t voi df=(n−1) 1−α α −t n−1, P ỗ ❣✐↔♥❣ ❳→❝ s✉➜t ❚❤è♥❣ ❦➯ ✈➔ ù♥❣ ❞ö♥❣ α t n−1, α