Statistik Inferensi I:
Estimasi & Confidence Interval

import numpy as np
import pandas as pd
from scipy import stats

# ── Dataset: Nilai UAS sampel mahasiswa ──────────────
np.random.seed(42)
nilai_sampel = np.random.normal(loc=78, scale=12, size=36)

n    = len(nilai_sampel)
xbar = np.mean(nilai_sampel)
s    = np.std(nilai_sampel, ddof=1)  # ddof=1 untuk std sampel
se   = s / np.sqrt(n)              # standard error

print(f"Ukuran Sampel  (n) : {n}")
print(f"Mean Sampel   (x̄) : {xbar:.2f}")
print(f"Std Deviasi    (s) : {s:.2f}")
print(f"Standard Error(SE) : {se:.2f}")

# ── Hitung CI dengan scipy.stats.t.interval ──────────
ci_90 = stats.t.interval(confidence=0.90, df=n-1, loc=xbar, scale=se)
ci_95 = stats.t.interval(confidence=0.95, df=n-1, loc=xbar, scale=se)
ci_99 = stats.t.interval(confidence=0.99, df=n-1, loc=xbar, scale=se)

print("\n═══ CONFIDENCE INTERVALS ═══")
print(f"90% CI : [{ci_90[0]:.2f} , {ci_90[1]:.2f}]  (lebar: {ci_90[1]-ci_90[0]:.2f})")
print(f"95% CI : [{ci_95[0]:.2f} , {ci_95[1]:.2f}]  (lebar: {ci_95[1]-ci_95[0]:.2f})")
print(f"99% CI : [{ci_99[0]:.2f} , {ci_99[1]:.2f}]  (lebar: {ci_99[1]-ci_99[0]:.2f})")

from statsmodels.stats.proportion import proportion_confint

# Contoh: dari 200 mahasiswa, 130 lulus tepat waktu
# Estimasi proporsi kelulusan tepat waktu populasi
n_sukses = 130    # jumlah sukses (lulus tepat waktu)
n_total  = 200    # total sampel
p_hat    = n_sukses / n_total  # proporsi sampel

print(f"Proporsi sampel (p̂) : {p_hat:.2%}")

# 95% CI untuk proporsi (metode Wilson)
ci_low, ci_high = proportion_confint(
    count=n_sukses, nobs=n_total, 
    alpha=0.05, method='wilson'
)

print(f"95% CI Proporsi: [{ci_low:.2%} , {ci_high:.2%}]")
print("\nKesimpulan:")
print(f"Kita 95% yakin bahwa proporsi kelulusan tepat waktu")
print(f"di seluruh populasi berada antara {ci_low:.1%} - {ci_high:.1%}")

import matplotlib.pyplot as plt

# Simulasi: bagaimana CI berubah seiring bertambahnya n
ukuran_n = [10, 20, 30, 50, 100, 200, 500]
lebar_ci = []

for n in ukuran_n:
    sampel = np.random.normal(78, 12, n)
    ci = stats.t.interval(0.95, df=n-1, loc=sampel.mean(), scale=stats.sem(sampel))
    lebar_ci.append(ci[1] - ci[0])

plt.figure(figsize=(9, 5))
plt.plot(ukuran_n, lebar_ci, 'o-', color='#3B82F6', linewidth=2, markersize=8)
plt.fill_between(ukuran_n, lebar_ci, alpha=0.15, color='#3B82F6')
plt.title('Lebar 95% CI vs Ukuran Sampel (n)\nSemakin besar n → CI makin sempit → makin presisi')
plt.xlabel('Ukuran Sampel (n)')
plt.ylabel('Lebar CI')
plt.grid(alpha=0.3)
plt.tight_layout()
plt.show()