1from scipy import stats
2import numpy as np
3
4# Dữ liệu mẫu
5sample = [192, 198, 190, 195, 202, 188, 197, 194, 199, 195]
6
7# H₀: μ = 200, H₁: μ ≠ 200
8mu_0 = 200
9alpha = 0.05
10
11# One-sample t-test
12t_stat, p_value = stats.ttest_1samp(sample, mu_0)
13
14print(f"Sample mean: {np.mean(sample):.2f}")
15print(f"Sample std: {np.std(sample, ddof=1):.2f}")
16print(f"t-statistic: {t_stat:.4f}")
17print(f"P-value: {p_value:.4f}")
18print(f"df: {len(sample) - 1}")
19
20if p_value < alpha:
21    print(f"\n→ Reject H₀: Mean khác 200mg")
22else:
23    print(f"\n→ Fail to Reject H₀: Không đủ bằng chứng")

1import numpy as np
2from scipy import stats
3
4sample = [192, 198, 190, 195, 202, 188, 197, 194, 199, 195]
5mu_0 = 200
6
7n = len(sample)
8x_bar = np.mean(sample)
9s = np.std(sample, ddof=1)
10df = n - 1
11
12# T-statistic
13t = (x_bar - mu_0) / (s / np.sqrt(n))
14print(f"t = {t:.4f}")
15
16# P-value (two-tailed)
17p_value = 2 * (1 - stats.t.cdf(abs(t), df))
18print(f"P-value = {p_value:.4f}")
19
20# Critical value
21t_critical = stats.t.ppf(0.975, df)
22print(f"Critical value (α=0.05): ±{t_critical:.4f}")

1from scipy import stats
2import numpy as np
3
4# Dữ liệu
5class_A = [85, 90, 78, 92, 88, 76, 95, 89, 82, 91]
6class_B = [72, 85, 80, 78, 88, 70, 82, 75, 79, 84]
7
8alpha = 0.05
9
10# H₀: μ_A = μ_B, H₁: μ_A ≠ μ_B
11
12# Descriptive stats
13print("Class A:", f"mean={np.mean(class_A):.2f}, std={np.std(class_A, ddof=1):.2f}")
14print("Class B:", f"mean={np.mean(class_B):.2f}, std={np.std(class_B, ddof=1):.2f}")
15
16# Independent t-test (equal variances assumed)
17t_stat, p_value = stats.ttest_ind(class_A, class_B)
18print(f"\nt-statistic: {t_stat:.4f}")
19print(f"P-value: {p_value:.4f}")
20
21# Welch's t-test (unequal variances)
22t_stat_welch, p_value_welch = stats.ttest_ind(class_A, class_B, equal_var=False)
23print(f"\nWelch's t-test:")
24print(f"t-statistic: {t_stat_welch:.4f}")
25print(f"P-value: {p_value_welch:.4f}")
26
27if p_value < alpha:
28    print(f"\n→ Reject H₀: Hai lớp có điểm khác nhau")
29else:
30    print(f"\n→ Fail to Reject H₀: Không đủ bằng chứng")

1from scipy import stats
2
3# Levene's test
4# H₀: σ₁² = σ₂²
5stat, p_value = stats.levene(class_A, class_B)
6print(f"Levene's test: stat={stat:.4f}, p-value={p_value:.4f}")
7
8if p_value > 0.05:
9    print("→ Variances are equal, use standard t-test")
10else:
11    print("→ Variances are unequal, use Welch's t-test")

1from scipy import stats
2import numpy as np
3
4# Dữ liệu (same subjects)
5before = [85, 90, 78, 92, 88, 76, 95, 89, 82, 91]
6after = [82, 86, 75, 88, 84, 74, 90, 85, 79, 87]
7
8alpha = 0.05
9
10# H₀: μ_diff = 0 (không thay đổi)
11# H₁: μ_diff ≠ 0 (có thay đổi)
12
13# Calculate differences
14differences = np.array(before) - np.array(after)
15print(f"Differences: {differences}")
16print(f"Mean difference: {np.mean(differences):.2f}")
17
18# Paired t-test
19t_stat, p_value = stats.ttest_rel(before, after)
20print(f"\nt-statistic: {t_stat:.4f}")
21print(f"P-value: {p_value:.4f}")
22
23if p_value < alpha:
24    print(f"\n→ Reject H₀: Chương trình có hiệu quả")
25else:
26    print(f"\n→ Fail to Reject H₀: Không đủ bằng chứng")

1from scipy import stats
2import numpy as np
3
4# Tung xúc xắc 600 lần
5observed = [95, 105, 98, 110, 92, 100]  # Số lần mỗi mặt
6expected = [100] * 6  # Expected nếu fair
7
8# Chi-square test
9chi2, p_value = stats.chisquare(observed, expected)
10
11print(f"Observed: {observed}")
12print(f"Expected: {expected}")
13print(f"\nChi-square: {chi2:.4f}")
14print(f"P-value: {p_value:.4f}")
15print(f"df: {len(observed) - 1}")
16
17if p_value < 0.05:
18    print("\n→ Reject H₀: Xúc xắc không cân")
19else:
20    print("\n→ Fail to Reject H₀: Xúc xắc có vẻ cân")

1from scipy import stats
2import numpy as np
3import pandas as pd
4
5# Contingency table
6observed = np.array([[30, 45],   # Male: A, B
7                     [40, 35]])  # Female: A, B
8
9# Chi-square test of independence
10chi2, p_value, dof, expected = stats.chi2_contingency(observed)
11
12print("=== Observed ===")
13print(pd.DataFrame(observed, 
14                   index=['Male', 'Female'], 
15                   columns=['Prefer A', 'Prefer B']))
16
17print("\n=== Expected ===")
18print(pd.DataFrame(expected.round(2), 
19                   index=['Male', 'Female'], 
20                   columns=['Prefer A', 'Prefer B']))
21
22print(f"\nChi-square: {chi2:.4f}")
23print(f"P-value: {p_value:.4f}")
24print(f"Degrees of freedom: {dof}")
25
26if p_value < 0.05:
27    print("\n→ Reject H₀: Giới tính và preference có liên quan")
28else:
29    print("\n→ Fail to Reject H₀: Không có mối liên hệ")

1def cramers_v(contingency_table):
2    chi2, p, dof, expected = stats.chi2_contingency(contingency_table)
3    n = contingency_table.sum()
4    min_dim = min(contingency_table.shape) - 1
5    return np.sqrt(chi2 / (n * min_dim))
6
7v = cramers_v(observed)
8print(f"Cramér's V: {v:.4f}")
9
10# Interpretation
11if v < 0.1:
12    print("→ Negligible association")
13elif v < 0.3:
14    print("→ Small association")
15elif v < 0.5:
16    print("→ Medium association")
17else:
18    print("→ Large association")

1from scipy import stats
2
3# Kiểm tra normality
4data = [85, 90, 78, 92, 88, 76, 95, 89, 82, 91]
5stat, p_value = stats.shapiro(data)
6print(f"Shapiro-Wilk: stat={stat:.4f}, p={p_value:.4f}")
7if p_value > 0.05:
8    print("→ Data is approximately normal")