# Step 1: Import the tools we need
import numpy as np
from scipy import stats
import matplotlib.pyplot as plt

# Step 2: Enter your data
n = 200                    # Sample size (products inspected)
x = 15                     # Number of successes (defective products)
p_hat = x / n              # Sample proportion
p_0 = 0.05                 # Claimed proportion
alpha = 0.05               # Significance level

print("🏭 DEFECTIVE PRODUCTS TEST")
print("="*60)
print(f"Sample size: {n} products")
print(f"Defective found: {x} products")
print(f"Sample proportion: {p_hat:.4f} ({p_hat*100:.2f}%)")
print(f"Claimed proportion: {p_0:.4f} ({p_0*100:.2f}%)")
print("="*60)

# Step 3: Check assumptions
np_0 = n * p_0
n_1_p_0 = n * (1 - p_0)

print(f"\n🔍 CHECKING ASSUMPTIONS:")
print(f"np₀ = {np_0:.1f} (need ≥ 10) {'✅' if np_0 >= 10 else '❌'}")
print(f"n(1-p₀) = {n_1_p_0:.1f} (need ≥ 10) {'✅' if n_1_p_0 >= 10 else '❌'}")

if np_0 >= 10 and n_1_p_0 >= 10:
    print("✅ Sample size is large enough! We can proceed.")
else:
    print("❌ Sample size too small! Results may not be reliable.")

# Step 4: Calculate Z-score
se = np.sqrt(p_0 * (1 - p_0) / n)  # Standard error
z_score = (p_hat - p_0) / se

print(f"\n📊 TEST RESULTS:")
print(f"Standard error: {se:.4f}")
print(f"Z-score: {z_score:.4f}")

# Step 5: Calculate p-value (one-tailed, right side)
p_value = 1 - stats.norm.cdf(z_score)
print(f"P-value (one-tailed): {p_value:.4f}")

# Step 6: Find critical value
z_critical = stats.norm.ppf(1 - alpha)
print(f"Critical value: {z_critical:.4f}")

# Step 7: Make a decision
print("\n🎯 DECISION:")
if p_value < alpha:
    print(f"✅ REJECT H₀: Defect rate IS higher than {p_0*100:.0f}%!")
    print(f"   (p-value {p_value:.4f} < {alpha})")
    print(f"   We found {p_hat*100:.1f}% defective, significantly higher than claimed")
else:
    print(f"❌ FAIL TO REJECT H₀: Not enough evidence")
    print(f"   (p-value {p_value:.4f} > {alpha})")
    print(f"   The {p_hat*100:.1f}% defect rate could be due to random variation")

# Step 8: Visualize
fig, axes = plt.subplots(1, 2, figsize=(14, 5))

# Plot 1: Bar chart comparing proportions
axes[0].bar(['Claimed', 'Observed'], [p_0, p_hat], color=['blue', 'red'], alpha=0.7)
axes[0].axhline(p_0, color='blue', linestyle='--', linewidth=2, label='Claimed rate')
axes[0].set_ylabel('Proportion Defective')
axes[0].set_title('Defect Rate Comparison')
axes[0].legend()
axes[0].grid(True, alpha=0.3, axis='y')

# Add percentage labels on bars
for i, (label, value) in enumerate([('Claimed', p_0), ('Observed', p_hat)]):
    axes[0].text(i, value + 0.005, f'{value*100:.1f}%', ha='center', fontweight='bold')

# Plot 2: Z-score distribution
x = np.linspace(-4, 4, 1000)
y = stats.norm.pdf(x)

axes[1].plot(x, y, 'b-', linewidth=2, label='Standard Normal')
axes[1].axvline(z_score, color='r', linestyle='--', linewidth=2, 
                label=f'Our Z-score = {z_score:.2f}')
axes[1].axvline(z_critical, color='g', linestyle='--', linewidth=1.5, 
                label=f'Critical value = {z_critical:.2f}')

# Shade rejection region
x_reject = np.linspace(z_critical, 4, 100)
axes[1].fill_between(x_reject, stats.norm.pdf(x_reject), alpha=0.3, color='red',
                     label='Rejection Region')

axes[1].set_xlabel('Z-score')
axes[1].set_ylabel('Probability Density')
axes[1].set_title('One-Sample Proportion Test (One-Tailed)')
axes[1].legend()
axes[1].grid(True, alpha=0.3)

plt.tight_layout()
plt.show()

print("\n📊 The graph shows our Z-score is just below the critical value!")

from statsmodels.stats.proportion import proportions_ztest

# Your data
count = 15        # Number of defective products
nobs = 200        # Total products inspected
value = 0.05      # Claimed proportion

# Perform one-sample proportion test
z_stat, p_value = proportions_ztest(count, nobs, value, alternative='larger')

print("🏭 QUICK PROPORTION TEST")
print("="*60)
print(f"Defective: {count} out of {nobs} ({count/nobs*100:.1f}%)")
print(f"Claimed: {value*100:.0f}%")
print(f"\nZ-statistic: {z_stat:.4f}")
print(f"P-value: {p_value:.4f}")

if p_value < 0.05:
    print("\n✅ Significant! Defect rate is higher than claimed.")
else:
    print("\n❌ Not significant. Could be random variation.")
print("="*60)

# Step 1: Import tools
import numpy as np
from scipy import stats
import matplotlib.pyplot as plt

# Step 2: Enter your data
# Version A
n1 = 500          # Visitors to Version A
x1 = 50           # Clicks on Version A
p1_hat = x1 / n1  # Click rate for Version A

# Version B
n2 = 500          # Visitors to Version B
x2 = 80           # Clicks on Version B
p2_hat = x2 / n2  # Click rate for Version B

alpha = 0.05      # Significance level

print("🖱️ A/B TESTING: WEBSITE CLICK RATES")
print("="*60)
print(f"Version A:")
print(f"  Visitors: {n1}")
print(f"  Clicks: {x1}")
print(f"  Click rate: {p1_hat:.4f} ({p1_hat*100:.1f}%)")
print(f"\nVersion B:")
print(f"  Visitors: {n2}")
print(f"  Clicks: {x2}")
print(f"  Click rate: {p2_hat:.4f} ({p2_hat*100:.1f}%)")
print(f"\nDifference: {(p2_hat - p1_hat)*100:.1f} percentage points")
print("="*60)

# Step 3: Calculate pooled proportion
p_pooled = (x1 + x2) / (n1 + n2)
print(f"\n📊 Pooled proportion: {p_pooled:.4f} ({p_pooled*100:.1f}%)")

# Step 4: Calculate standard error
se = np.sqrt(p_pooled * (1 - p_pooled) * (1/n1 + 1/n2))
print(f"Standard error: {se:.4f}")

# Step 5: Calculate Z-score
z_score = (p1_hat - p2_hat) / se
print(f"Z-score: {z_score:.4f}")

# Step 6: Calculate p-value (two-tailed)
p_value = 2 * stats.norm.cdf(z_score)  # Two-tailed (z_score is negative)
print(f"P-value (two-tailed): {p_value:.4f}")

# Step 7: Make a decision
print("\n🎯 DECISION:")
if p_value < alpha:
    print(f"✅ REJECT H₀: The versions ARE different!")
    print(f"   (p-value {p_value:.4f} < {alpha})")
    if p2_hat > p1_hat:
        print(f"   Version B is BETTER! ({p2_hat*100:.1f}% vs {p1_hat*100:.1f}%)")
        improvement = ((p2_hat - p1_hat) / p1_hat) * 100
        print(f"   That's a {improvement:.1f}% relative improvement!")
    else:
        print(f"   Version A is BETTER! ({p1_hat*100:.1f}% vs {p2_hat*100:.1f}%)")
else:
    print(f"❌ FAIL TO REJECT H₀: No significant difference")
    print(f"   (p-value {p_value:.4f} > {alpha})")
    print(f"   The difference could be random variation")

# Step 8: Visualize
fig, axes = plt.subplots(1, 2, figsize=(14, 5))

# Plot 1: Bar chart comparing proportions
versions = ['Version A', 'Version B']
click_rates = [p1_hat, p2_hat]
colors = ['blue', 'green']

bars = axes[0].bar(versions, click_rates, color=colors, alpha=0.7, edgecolor='black')
axes[0].set_ylabel('Click Rate')
axes[0].set_title('Click Rate Comparison')
axes[0].grid(True, alpha=0.3, axis='y')

# Add percentage labels on bars
for bar, rate in zip(bars, click_rates):
    height = bar.get_height()
    axes[0].text(bar.get_x() + bar.get_width()/2., height + 0.005,
                f'{rate*100:.1f}%', ha='center', va='bottom', fontweight='bold')

# Plot 2: Sample sizes and success rates
x_pos = np.arange(2)
successes = [x1, x2]
failures = [n1-x1, n2-x2]

axes[1].bar(x_pos, successes, label='Clicks', color='green', alpha=0.7)
axes[1].bar(x_pos, failures, bottom=successes, label='No Clicks', color='gray', alpha=0.7)
axes[1].set_xticks(x_pos)
axes[1].set_xticklabels(versions)
axes[1].set_ylabel('Number of Visitors')
axes[1].set_title('Clicks vs No Clicks')
axes[1].legend()
axes[1].grid(True, alpha=0.3, axis='y')

plt.tight_layout()
plt.show()

print("\n📊 The graphs show Version B has a higher click rate!")

from statsmodels.stats.proportion import proportions_ztest

# Your data
count = np.array([50, 80])      # Clicks for each version
nobs = np.array([500, 500])     # Visitors for each version

# Perform two-sample proportion test
z_stat, p_value = proportions_ztest(count, nobs)

print("🖱️ QUICK A/B TEST")
print("="*60)
print(f"Version A: {count[0]} clicks out of {nobs[0]} ({count[0]/nobs[0]*100:.1f}%)")
print(f"Version B: {count[1]} clicks out of {nobs[1]} ({count[1]/nobs[1]*100:.1f}%)")
print(f"\nZ-statistic: {z_stat:.4f}")
print(f"P-value: {p_value:.4f}")

if p_value < 0.05:
    print("\n✅ Significant difference! The versions perform differently.")
    if count[1]/nobs[1] > count[0]/nobs[0]:
        print("   Version B is the winner! 🎉")
    else:
        print("   Version A is the winner! 🎉")
else:
    print("\n❌ No significant difference. Keep testing or stick with current version.")
print("="*60)

import numpy as np
from scipy import stats
from statsmodels.stats.proportion import proportions_ztest
import matplotlib.pyplot as plt

# Data
n = 100           # Number of flips
heads = 60        # Number of heads
p_hat = heads / n # Sample proportion
p_0 = 0.5         # Fair coin proportion

print("🪙 COIN FAIRNESS TEST")
print("="*60)
print(f"Flips: {n}")
print(f"Heads: {heads} ({p_hat*100:.0f}%)")
print(f"Expected (fair coin): {p_0*100:.0f}%")
print("="*60)

# Perform test
z_stat, p_value = proportions_ztest(heads, n, p_0)

print(f"\n📊 TEST RESULTS:")
print(f"Z-statistic: {z_stat:.4f}")
print(f"P-value (two-tailed): {p_value:.4f}")

print("\n🎯 DECISION:")
if p_value < 0.05:
    print(f"✅ REJECT H₀: The coin IS biased!")
    print(f"   (p-value {p_value:.4f} < 0.05)")
    if p_hat > 0.5:
        print(f"   It favors HEADS ({p_hat*100:.0f}%)")
    else:
        print(f"   It favors TAILS ({(1-p_hat)*100:.0f}%)")
else:
    print(f"❌ FAIL TO REJECT H₀: The coin appears fair")
    print(f"   (p-value {p_value:.4f} > 0.05)")
    print(f"   The {p_hat*100:.0f}% heads could be random variation")

# Visualize
fig, axes = plt.subplots(1, 2, figsize=(14, 5))

# Plot 1: Pie chart of results
axes[0].pie([heads, n-heads], labels=['Heads', 'Tails'], autopct='%1.0f%%',
            colors=['gold', 'silver'], startangle=90)
axes[0].set_title(f'Coin Flip Results (n={n})')

# Plot 2: Bar chart comparing to fair coin
axes[1].bar(['Expected\n(Fair Coin)', 'Observed'], [0.5, p_hat], 
            color=['blue', 'red'], alpha=0.7, edgecolor='black')
axes[1].axhline(0.5, color='blue', linestyle='--', linewidth=2, label='Fair coin (50%)')
axes[1].set_ylabel('Proportion of Heads')
axes[1].set_title('Expected vs Observed')
axes[1].legend()
axes[1].grid(True, alpha=0.3, axis='y')

plt.tight_layout()
plt.show()

import numpy as np
from scipy import stats
from statsmodels.stats.proportion import proportions_ztest
import matplotlib.pyplot as plt

# Data
n_men = 400
prefer_men = 120
p_men = prefer_men / n_men

n_women = 400
prefer_women = 160
p_women = prefer_women / n_women

print("👨👩 GENDER PREFERENCE ANALYSIS")
print("="*60)
print(f"Men:")
print(f"  Sample size: {n_men}")
print(f"  Prefer product: {prefer_men} ({p_men*100:.1f}%)")
print(f"\nWomen:")
print(f"  Sample size: {n_women}")
print(f"  Prefer product: {prefer_women} ({p_women*100:.1f}%)")
print(f"\nDifference: {(p_women - p_men)*100:.1f} percentage points")
print("="*60)

# Perform test
count = np.array([prefer_men, prefer_women])
nobs = np.array([n_men, n_women])
z_stat, p_value = proportions_ztest(count, nobs)

print(f"\n📊 TEST RESULTS:")
print(f"Z-statistic: {z_stat:.4f}")
print(f"P-value (two-tailed): {p_value:.4f}")

print("\n🎯 DECISION:")
if p_value < 0.05:
    print(f"✅ REJECT H₀: There IS a gender difference!")
    print(f"   (p-value {p_value:.4f} < 0.05)")
    if p_women > p_men:
        print(f"   Women prefer it MORE ({p_women*100:.1f}% vs {p_men*100:.1f}%)")
    else:
        print(f"   Men prefer it MORE ({p_men*100:.1f}% vs {p_women*100:.1f}%)")
else:
    print(f"❌ FAIL TO REJECT H₀: No significant gender difference")
    print(f"   (p-value {p_value:.4f} > 0.05)")

# Visualize
fig, axes = plt.subplots(1, 2, figsize=(14, 5))

# Plot 1: Grouped bar chart
x = np.arange(2)
width = 0.35

prefer = [prefer_men, prefer_women]
not_prefer = [n_men - prefer_men, n_women - prefer_women]

axes[0].bar(x - width/2, prefer, width, label='Prefer', color='green', alpha=0.7)
axes[0].bar(x + width/2, not_prefer, width, label='Don\'t Prefer', color='red', alpha=0.7)
axes[0].set_xticks(x)
axes[0].set_xticklabels(['Men', 'Women'])
axes[0].set_ylabel('Number of People')
axes[0].set_title('Product Preference by Gender')
axes[0].legend()
axes[0].grid(True, alpha=0.3, axis='y')

# Plot 2: Proportion comparison
axes[1].bar(['Men', 'Women'], [p_men, p_women], color=['blue', 'pink'], 
            alpha=0.7, edgecolor='black')
axes[1].set_ylabel('Proportion Who Prefer Product')
axes[1].set_title('Preference Rate Comparison')
axes[1].grid(True, alpha=0.3, axis='y')

# Add percentage labels
for i, (label, value) in enumerate([('Men', p_men), ('Women', p_women)]):
    axes[1].text(i, value + 0.01, f'{value*100:.1f}%', ha='center', fontweight='bold')

plt.tight_layout()
plt.show()

import numpy as np
from statsmodels.stats.proportion import proportions_ztest
import matplotlib.pyplot as plt

# Data
n_before = 1000
convert_before = 80
p_before = convert_before / n_before

n_after = 1000
convert_after = 120
p_after = convert_after / n_after

print("📈 MARKETING CAMPAIGN EFFECTIVENESS")
print("="*60)
print(f"Before Campaign:")
print(f"  Visitors: {n_before}")
print(f"  Conversions: {convert_before} ({p_before*100:.1f}%)")
print(f"\nAfter Campaign:")
print(f"  Visitors: {n_after}")
print(f"  Conversions: {convert_after} ({p_after*100:.1f}%)")
print(f"\nImprovement: {(p_after - p_before)*100:.1f} percentage points")

# Calculate relative improvement
relative_improvement = ((p_after - p_before) / p_before) * 100
print(f"Relative improvement: {relative_improvement:.1f}%")
print("="*60)

# Perform test (one-tailed: we only care if it improved)
count = np.array([convert_before, convert_after])
nobs = np.array([n_before, n_after])
z_stat, p_value_two = proportions_ztest(count, nobs)
p_value_one = p_value_two / 2  # One-tailed

print(f"\n📊 TEST RESULTS:")
print(f"Z-statistic: {z_stat:.4f}")
print(f"P-value (one-tailed): {p_value_one:.4f}")

print("\n🎯 DECISION:")
if p_value_one < 0.05 and z_stat < 0:  # z_stat negative means after > before
    print(f"✅ REJECT H₀: Campaign WORKED!")
    print(f"   (p-value {p_value_one:.4f} < 0.05)")
    print(f"   Conversion rate improved from {p_before*100:.1f}% to {p_after*100:.1f}%")
    print(f"   That's a {relative_improvement:.1f}% relative improvement! 🎉")
else:
    print(f"❌ FAIL TO REJECT H₀: No significant improvement")
    print(f"   (p-value {p_value_one:.4f} > 0.05)")

# Visualize
fig, axes = plt.subplots(1, 2, figsize=(14, 5))

# Plot 1: Conversion rates
axes[0].bar(['Before', 'After'], [p_before, p_after], 
            color=['red', 'green'], alpha=0.7, edgecolor='black')
axes[0].set_ylabel('Conversion Rate')
axes[0].set_title('Conversion Rate: Before vs After Campaign')
axes[0].grid(True, alpha=0.3, axis='y')

# Add percentage labels and arrow
for i, (label, value) in enumerate([('Before', p_before), ('After', p_after)]):
    axes[0].text(i, value + 0.005, f'{value*100:.1f}%', ha='center', fontweight='bold')

# Add improvement arrow
axes[0].annotate('', xy=(1, p_after), xytext=(0, p_before),
                arrowprops=dict(arrowstyle='->', lw=2, color='blue'))
axes[0].text(0.5, (p_before + p_after)/2, f'+{(p_after-p_before)*100:.1f}pp',
            ha='center', fontweight='bold', color='blue', fontsize=12)

# Plot 2: Stacked bar showing conversions
periods = ['Before', 'After']
conversions = [convert_before, convert_after]
non_conversions = [n_before - convert_before, n_after - convert_after]

axes[1].bar(periods, conversions, label='Converted', color='green', alpha=0.7)
axes[1].bar(periods, non_conversions, bottom=conversions, 
            label='Did Not Convert', color='gray', alpha=0.7)
axes[1].set_ylabel('Number of Visitors')
axes[1].set_title('Conversions: Before vs After')
axes[1].legend()
axes[1].grid(True, alpha=0.3, axis='y')

plt.tight_layout()
plt.show()

# Write your code here!
# Hint: Claimed proportion = 1/6 ≈ 0.1667

# Write your code here!

import numpy as np
from statsmodels.stats.proportion import proportions_ztest

# Example: Test if success rate meets target
print("MY ONE-SAMPLE PROPORTION TEST")
print("="*60)
print("Scenario: [Describe your situation]")
print("Claimed proportion: [e.g., 50%]")
print("="*60)

# Your data
# n = ...           # Sample size
# successes = ...   # Number of successes
# p_0 = ...         # Claimed proportion

# Run test
# z_stat, p_value = proportions_ztest(successes, n, p_0)

# Make conclusion

import numpy as np
from statsmodels.stats.proportion import proportions_ztest

# Example: Compare two groups
print("MY TWO-SAMPLE PROPORTION TEST")
print("="*60)
print("Scenario: [Describe your comparison]")
print("="*60)

# Your data
# count = np.array([successes_group1, successes_group2])
# nobs = np.array([n_group1, n_group2])

# Run test
# z_stat, p_value = proportions_ztest(count, nobs)

# Make conclusion

from statsmodels.stats.proportion import proportions_ztest
import numpy as np

# One-Sample Proportion Test
count = 60        # Number of successes
nobs = 100        # Sample size
value = 0.5       # Claimed proportion
z_stat, p_value = proportions_ztest(count, nobs, value)

# Two-Sample Proportion Test
count = np.array([50, 80])      # Successes in each group
nobs = np.array([500, 500])     # Sample sizes
z_stat, p_value = proportions_ztest(count, nobs)

# One-tailed test (add alternative parameter)
z_stat, p_value = proportions_ztest(count, nobs, value, 
                                    alternative='larger')  # or 'smaller'

# Decision
if p_value < 0.05:
    print("Significant difference found!")
else:
    print("No significant difference")