Sampling và Sampling Distribution

1import numpy as np
2
3population = list(range(1, 1001))  # 1000 người
4sample = np.random.choice(population, size=100, replace=False)
5print(f"Sample size: {len(sample)}")
6print(f"First 10: {sample[:10]}")

1import pandas as pd
2import numpy as np
3
4# Giả sử có 60% nam, 40% nữ
5np.random.seed(42)
6population = pd.DataFrame({
7    'id': range(1000),
8    'gender': np.random.choice(['M', 'F'], 1000, p=[0.6, 0.4])
9})
10
11# Stratified sampling: lấy 10% từ mỗi nhóm
12sample = population.groupby('gender').apply(
13    lambda x: x.sample(frac=0.1)
14).reset_index(drop=True)
15
16print(f"Sample size: {len(sample)}")
17print(sample['gender'].value_counts())

1population = list(range(1, 1001))
2n = 100
3k = len(population) // n  # k = 10
4
5# Chọn điểm bắt đầu ngẫu nhiên
6start = np.random.randint(0, k)
7systematic_sample = population[start::k]
8print(f"Sample size: {len(systematic_sample)}")

1import numpy as np
2import matplotlib.pyplot as plt
3
4# Population (không normal - uniform)
5np.random.seed(42)
6population = np.random.uniform(0, 100, 100000)
7pop_mean = np.mean(population)
8pop_std = np.std(population)
9
10print(f"Population Mean: {pop_mean:.2f}")
11print(f"Population Std: {pop_std:.2f}")
12
13# Lấy nhiều samples và tính mean
14sample_sizes = [10, 30, 100]
15fig, axes = plt.subplots(1, 3, figsize=(15, 4))
16
17for i, n in enumerate(sample_sizes):
18    sample_means = [np.mean(np.random.choice(population, n)) for _ in range(1000)]
19    
20    axes[i].hist(sample_means, bins=30, density=True, alpha=0.7)
21    axes[i].axvline(pop_mean, color='red', linestyle='--', label=f'μ = {pop_mean:.1f}')
22    axes[i].set_title(f'n = {n}\nSE = {pop_std/np.sqrt(n):.2f}')
23    axes[i].legend()
24
25plt.suptitle('Sampling Distribution of the Mean')
26plt.tight_layout()
27plt.show()

1import numpy as np
2
3def calculate_se(data=None, sigma=None, n=None):
4    """Tính Standard Error"""
5    if data is not None:
6        return np.std(data, ddof=1) / np.sqrt(len(data))
7    elif sigma is not None and n is not None:
8        return sigma / np.sqrt(n)
9    else:
10        raise ValueError("Cần cung cấp data hoặc (sigma, n)")
11
12# Ví dụ
13sample = [45, 52, 48, 55, 50, 53, 47, 51, 49, 54]
14se = calculate_se(data=sample)
15print(f"SE from sample: {se:.4f}")
16
17# Nếu biết population std
18se_known = calculate_se(sigma=10, n=100)
19print(f"SE with known σ: {se_known:.4f}")

1import numpy as np
2from scipy import stats
3
4p = 0.52
5n = 500
6
7SE = np.sqrt(p * (1-p) / n)
8print(f"SE = {SE:.4f}")
9
10# P(p̂ > 0.55)?
11z = (0.55 - p) / SE
12prob = 1 - stats.norm.cdf(z)
13print(f"P(p̂ > 0.55) = {prob:.4f}")

1from scipy import stats
2import numpy as np
3
4def sample_size_mean(sigma, margin_error, confidence=0.95):
5    """Tính sample size cho mean"""
6    z = stats.norm.ppf((1 + confidence) / 2)
7    n = (z * sigma / margin_error) ** 2
8    return int(np.ceil(n))
9
10def sample_size_proportion(margin_error, confidence=0.95, p=0.5):
11    """Tính sample size cho proportion"""
12    z = stats.norm.ppf((1 + confidence) / 2)
13    n = z**2 * p * (1-p) / margin_error**2
14    return int(np.ceil(n))
15
16# Ví dụ: Mean
17# σ = 15, margin of error = 3, 95% confidence
18n_mean = sample_size_mean(sigma=15, margin_error=3, confidence=0.95)
19print(f"Sample size for mean: {n_mean}")
20
21# Ví dụ: Proportion
22# Margin of error = 3%, 95% confidence
23n_prop = sample_size_proportion(margin_error=0.03, confidence=0.95)
24print(f"Sample size for proportion: {n_prop}")