import numpy as np
import scipy.stats as stats

def ab_test(n_A, conv_A, n_B, conv_B, alpha=0.05):
    """
    Conducts an A/B test using a Z-test for proportions.
    
    Parameters:
    n_A: Number of visitors in group A
    conv_A: Number of conversions in group A
    n_B: Number of visitors in group B
    conv_B: Number of conversions in group B
    alpha: Significance level (default 0.05)
    """
    # Calculate conversion rates
    p_A = conv_A / n_A
    p_B = conv_B / n_B
    
    # Combined conversion rate
    p_combined = (conv_A + conv_B) / (n_A + n_B)
    
    # Standard error
    SE = np.sqrt(p_combined * (1 - p_combined) * (1/n_A + 1/n_B))
    
    # Z-score
    Z = (p_B - p_A) / SE
    
    # p-value (one-sided test, checking if B > A)
    p_value = 1 - stats.norm.cdf(Z)
    
    # Confidence interval (95%)
    Z_alpha = stats.norm.ppf(1 - alpha/2)
    CI_lower = (p_B - p_A) - Z_alpha * SE
    CI_upper = (p_B - p_A) + Z_alpha * SE
    
    # Results
    print(f"Conversion rate A: {p_A:.4f}")
    print(f"Conversion rate B: {p_B:.4f}")
    print(f"Z-score: {Z:.4f}")
    print(f"p-value: {p_value:.4f}")
    print(f"95% confidence interval: ({CI_lower:.4f}, {CI_upper:.4f})")
    
    # Conclusion
    if p_value < alpha:
        print("➡️  Statistically significant difference! Implement version B.")
    else:
        print("➡️  No statistically significant difference.")

# Example data: Group A (5000 visitors, 250 conversions) and Group B (5000 visitors, 300 conversions)
ab_test(n_A=5000, conv_A=250, n_B=5000, conv_B=300)