Hypothesis Testing TypeTypeError Procedures of Hypothesis Testing Sample

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假說檢定(Hypothesis Testing) 型Ⅰ與型Ⅱ錯誤(TypeⅠ&TypeⅡError) 假說檢定之步驟(Procedures of Hypothesis Testing) 樣品數之決定(Sample Size Determination) 2 2020/10/26 Jen-pei Liu,

假說檢定(Hypothesis Testing) 型Ⅰ與型Ⅱ錯誤(TypeⅠ&TypeⅡError) 假說檢定之步驟(Procedures of Hypothesis Testing) 樣品數之決定(Sample Size Determination) 2 2020/10/26 Jen-pei Liu, Ph. D

vs. 9 平均每公頃產量增加 1000 kg/ha Ho：μ� 1000 kg/ha Ha：μ� 1000 kg/ha 奶粉重量不足 500公克 Ho：μ�

vs. 9 平均每公頃產量增加 1000 kg/ha Ho：μ� 1000 kg/ha Ha：μ� 1000 kg/ha 奶粉重量不足 500公克 Ho：μ� 500 g Ha：μ� 500 g 2020/10/26 Jen-pei Liu, Ph. D

型Ⅰ與型Ⅱ錯誤(TypeⅠ&TypeⅡError) 事實(Truth) 11 決策(Decision) Ho：μ 500 g為真 Ha：μ 500 g為真 不拒絕Ho Not reject Ho

型Ⅰ與型Ⅱ錯誤(TypeⅠ&TypeⅡError) 事實(Truth) 11 決策(Decision) Ho：μ 500 g為真 Ha：μ 500 g為真 不拒絕Ho Not reject Ho 決策正確 型Ⅱ錯誤 拒絕Ho Reject Ho 型Ⅰ錯誤 決策正確 2020/10/26 Jen-pei Liu, Ph. D

棄卻域 0 22 2020/10/26 Jen-pei Liu, Ph. D

棄卻域 0 22 2020/10/26 Jen-pei Liu, Ph. D

單尾檢定：對立假說是單一方向 Ho：μ μo(500 g) vs. Ha：μ μo(500 g) 若 =>拒絕Ho Ho：μ μo(1000 kg/ha) vs.

單尾檢定：對立假說是單一方向 Ho：μ μo(500 g) vs. Ha：μ μo(500 g) 若 =>拒絕Ho Ho：μ μo(1000 kg/ha) vs. Ha：μ μo(1000 kg/ha) 若 24 =>拒絕Ho 2020/10/26 Jen-pei Liu, Ph. D

例：奶粉罐重量 Ho：μ 500 g vs. Ha： μ 500 g 若α=0. 05，拒絕Ho 35 2020/10/26 Jen-pei

例：奶粉罐重量 Ho：μ 500 g vs. Ha： μ 500 g 若α=0. 05，拒絕Ho 35 2020/10/26 Jen-pei Liu, Ph. D

0. 05 0. 0013 485 36 490. 13 μo=500 g 2020/10/26 Jen-pei Liu, Ph.

0. 05 0. 0013 485 36 490. 13 μo=500 g 2020/10/26 Jen-pei Liu, Ph. D

485 37 490 495 μo=500 g 2020/10/26 Jen-pei Liu, Ph. D

485 37 490 495 μo=500 g 2020/10/26 Jen-pei Liu, Ph. D

統計假說檢定或顯著性檢定(Statistical Hypothesis Testing or Significance Test) 5. 決策判定: l 顯著水準定為 0. 05(1/20) 樣本平均值 p-value

統計假說檢定或顯著性檢定(Statistical Hypothesis Testing or Significance Test) 5. 決策判定: l 顯著水準定為 0. 05(1/20) 樣本平均值 p-value 決策判定 495 0. 1587 不顯著(無法推翻虛無假說) 490 0. 0228 顯著(推翻虛無假說) 485 0. 0013 顯著(推翻虛無假說) l 38 2020/10/26 Jen-pei Liu, Ph. D

統計假說檢定或顯著性檢定(Statistical Hypothesis Testing or Significance Test) 5. 決策判定: l 顯著水準定為 0. 20(1/5) 樣本平均值 p-value

統計假說檢定或顯著性檢定(Statistical Hypothesis Testing or Significance Test) 5. 決策判定: l 顯著水準定為 0. 20(1/5) 樣本平均值 p-value 決策判定 495 0. 1587 顯著(推翻虛無假說) 490 0. 0228 顯著(推翻虛無假說) 485 0. 0013 顯著(推翻虛無假說) l 39 2020/10/26 Jen-pei Liu, Ph. D

例：膽固醇 Ho：μ=180 mg/d. L vs. Ha： μ 180 mg/d. L 雙尾檢定 若α=0. 05，無法拒絕Ho 41

例：膽固醇 Ho：μ=180 mg/d. L vs. Ha： μ 180 mg/d. L 雙尾檢定 若α=0. 05，無法拒絕Ho 41 2020/10/26 Jen-pei Liu, Ph. D

例：奶粉罐重量 Ho：μ 500 g vs. Ha： μ 500 g 在 5%顯著水準下，拒絕Ho 45 2020/10/26 Jen-pei

例：奶粉罐重量 Ho：μ 500 g vs. Ha： μ 500 g 在 5%顯著水準下，拒絕Ho 45 2020/10/26 Jen-pei Liu, Ph. D

例：膽固醇 Ho：μ=180 mg/d. L vs. Ha： μ 180 mg/d. L =>在 5%顯著水準下， 無法拒絕Ho 46

例：膽固醇 Ho：μ=180 mg/d. L vs. Ha： μ 180 mg/d. L =>在 5%顯著水準下， 無法拒絕Ho 46 2020/10/26 Jen-pei Liu, Ph. D

統計顯著vs. 應用顯著vs. 樣本數 樣本平均值=499 g, 母體平均值=500 g 樣本平均值 -母體平均值 = -1 g 母體標準偏差=30 g

統計顯著vs. 應用顯著vs. 樣本數 樣本平均值=499 g, 母體平均值=500 g 樣本平均值 -母體平均值 = -1 g 母體標準偏差=30 g 樣本數 / n z p-value 100 3 -0. 33 0. 3707 1600 0. 75 -1. 33 0. 0918 3600 0. 5 -2 0. 0228 10000 0. 33 -3. 33 0. 0012 0 - 0 51 2020/10/26 Jen-pei Liu, Ph. D

485 55 490. 13 2020/10/26 500 Jen-pei Liu, Ph. D

485 55 490. 13 2020/10/26 500 Jen-pei Liu, Ph. D

α=0. 05 μo=500 1－β=0. 1587 57 490. 13 μa=496. 13 2020/10/26 Jen-pei Liu, Ph.

α=0. 05 μo=500 1－β=0. 1587 57 490. 13 μa=496. 13 2020/10/26 Jen-pei Liu, Ph. D

設 若 58 2020/10/26 Jen-pei Liu, Ph. D

設 若 58 2020/10/26 Jen-pei Liu, Ph. D

α=0. 10 μo=500 1－β=0. 263 μa=496. 13 59 492. 32 2020/10/26 Jen-pei Liu, Ph.

α=0. 10 μo=500 1－β=0. 263 μa=496. 13 59 492. 32 2020/10/26 Jen-pei Liu, Ph. D

若μa=484. 13 1－β=P[拒絕Ho∣ Ha為真] 60 2020/10/26 Jen-pei Liu, Ph. D

若μa=484. 13 1－β=P[拒絕Ho∣ Ha為真] 60 2020/10/26 Jen-pei Liu, Ph. D

α=0. 05 μo=500 1－β=0. 8413 61 μa=484. 13 2020/10/26 490. 13 Jen-pei Liu, Ph.

α=0. 05 μo=500 1－β=0. 8413 61 μa=484. 13 2020/10/26 490. 13 Jen-pei Liu, Ph. D

習題 l 67 P. 163: 1, 2, 6, 7 2020/10/26 Jen-pei Liu, Ph. D

習題 l 67 P. 163: 1, 2, 6, 7 2020/10/26 Jen-pei Liu, Ph. D

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