English: Distributions of sample means under the null (θ=0) and alternative hypotheses are shown. The shaded red area represents Type I error (α), held constant at 0.05, while the shaded green area represents statistical power (1-β). As the sample size increases, the distributions narrow, leading to clearer separation between the hypotheses and higher power. Similarly, a larger effect size increases the distance between the distributions, resulting in greater power.

```python import numpy as np import matplotlib.pyplot as plt from scipy.stats import norm

1. Parameters

alpha = 0.05 # Significance level

1. Create subplots

xmin, xmax = -0.4, 0.6 ns = [10, 30, 100] thetas = [0.1, 0.3, 0.5] fig, axes = plt.subplots(len(ns), len(thetas), figsize=(12, 10))

1. Loop through different scenarios

for i, n in enumerate(ns): # Sample sizes

   for j, theta in enumerate(thetas):  # Effect sizes
       # Calculate parameters
       sigma = 1 / np.sqrt(n)
       z_alpha = norm.ppf(1 - alpha)
       threshold = z_alpha * sigma
       power = 1 - norm.cdf(z_alpha - theta / sigma)

       # Generate distributions
       x = np.linspace(xmin, xmax, 1000)
       null_dist = norm.pdf(x, 0, sigma)
       alt_dist = norm.pdf(x, theta, sigma)

       # Plot on the corresponding subplot
       ax = axes[i, j]

ax.plot(x, null_dist, label=rf'$H_0\; (\theta = 0)