(interval estimation) 3 (confidence coefficient) µ σ/sqrt(n) 4 P ( (X - µ) / (σ sqrt N < a) = α a α X α µ a σ sqrt N X µ a σ sqrt N 2

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1 7 2 1

2 (interval estimation) 3 (confidence coefficient) µ σ/sqrt(n) 4 P ( (X - µ) / (σ sqrt N < a) = α a α X α µ a σ sqrt N X µ a σ sqrt N 2

3 (confidence interval) 5 X a σ sqrt N µ X a σ sqrt N - 6 P ( X / (σ sqrt N - µ < a) = α µ [ X a σ sqrt N X a σ sqrt N α α µ 3

4 % 99% 8 step 1: a) - 95% % step 2: /sqrt(100)=1.5 4

5 9 step3 step1, step2-95% [ x 1.5, x 1.5] = [62.1, 67.9] - 99% [ x 1.5, x 1.5] = [61.1, 68.9] 10 TOEFL H0: µ H1: µ

6 11 µ σ/sqrt(n) step 1: 100 / sqrt(1600) = 2.5 step 2: 5% - z 2 (1.96) x 2 step 3: 6

7 13 A % 14 - H0 µ H1 µ H0 µ = H1 µ > 100 7

8 % z x0.45= H0 µ =100 - H1 µ 100 5% 16 / sqrt(64) = 2 - z-score ( ) / 2 = 3 8

9 17 5% z-score % x 2 < µ < x : 2 : - 1 α 2 β 1 β - 9

10 % - H0 µ = 30 - H1 µ = step1: % step2: - =

11 21 22 ^ 1 σ 2 = Σ (X - X) 2 n

12 t (t - distribution) 23 Student t - t n ν - ν t t (ν). t 24 n n t n / n -2 - n - n n 1 12

13 (degrees of freedom) 25 - n 26 n n - 1 t ν t ν 2 ν Xi Xi 2 ν 2 X Y ν 2 Z = X / sqrt(y / ν) ν t 13

14 n S = Σ(X i - X) 2 n n - 1 tricky step 1: Y i (i n-1 0, σ 2 Y 1 = (X 1 - X 2 ) / sqrt(2), Y 2 = (X 1 + X 2-2X 3 )/sqrt(6), 27 step 2: X Y i step 3: Σ i Y i 2 + n X 2 Σ i X i2 S = Σ i X i 2 - n X 2 = Σ i Y i 2 step 4: step 1 Σ i (Y i /σ) 2 n-1 2 (Y i n-1 step 5: step 3 4 S / σ 2 n

15 29 - t , 117, 135, 128, 137, 127, 119, , 126, 131, 123, 130, 123, 135, 122 (cm) 130cm 1% 15

16 1 31 step1: - H0: µ = H1: µ 130 step 2: - X = σ σ ^ = σ Μ = 6.72 / sqrt(16) = step 3: - 1% - 15 t t , t step 4: t t = (X - µ) / σ Μ = ( ) / 1.68 = step 5: - 16

17 (30 ) t - (30 ) - (30 ) 17

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