7 2 1
(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
(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
7 15 100 65 95% 99% 8 step 1: a) - 95% 1.96. 99% 2.58. step 2: 15 100 15/sqrt(100)=1.5 4
9 step3 step1, step2-95% [65-1.96 x 1.5, 65 + 1.96 x 1.5] = [62.1, 67.9] - 99% [65-2.58 x 1.5, 65 + 2.58 x 1.5] = [61.1, 68.9] 10 TOEFL 500 100 500 - H0: µ 500 - H1: µ 500 100 5
11 µ σ/sqrt(n) 12 1600 507.2 step 1: 100 / sqrt(1600) = 2.5 step 2: 5% - z 2 (1.96) - 500 2.5 x 2 step 3: 6
13 A 100 9 400 101.5 5% 14 - H0 µ 100 - H1 µ 100 - H0 µ = 100 - H1 µ > 100 7
15 100 0.45-5% z 1.645-100+1.645x0.45=100.74-101.5 16 64 106 16 - H0 µ =100 - H1 µ 100 5% 16 / sqrt(64) = 2 - z-score (106-100) / 2 = 3 8
17 5% z-score 1.96 95% 106-1.96 x 2 < µ < 106 + 1.96 x 2-100 18 1 : 2 : - 1 α 2 β 1 β - 9
19 30 3 100 5% - H0 µ = 30 - H1 µ = 31 20 step1: - 100 0.3-5% 30.49 step2: - =0.9554 10
21 22 ^ 1 σ 2 = Σ (X - X) 2 n - 1 11
t (t - distribution) 23 Student t - t n ν - ν t t (ν). t 24 n n - 1 2 t n / n -2 - n - n n 1 12
(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
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 - 1 2 28 14
29 - t 30 16 115, 117, 135, 128, 137, 127, 119, 130 134, 126, 131, 123, 130, 123, 135, 122 (cm) 130cm 1% 15
1 31 step1: - H0: µ = 130 - H1: µ 130 step 2: - X = 127 - σ σ ^ = 6.72 - σ Μ = 6.72 / sqrt(16) = 1.68 2 32 step 3: - 1% - 15 t t -2.947, 2.947 t step 4: t t = (X - µ) / σ Μ = (127-130) / 1.68 = -1.79 step 5: - 16
33 - - (30 ) t - (30 ) - (30 ) 17