First, let's reload the CLT Simulator code available in the following link:

https://colab.research.google.com/drive/1xlPjna5F0L2hBNJjyapA-zF3Pu5vF6N7?usp=sharing

Additionally, the code about how to employ a Shapiro-Wilk is available in the following link:

https://colab.research.google.com/drive/1dLk4yeCrSnqs9ok2CoGnhJGAAb9QVzfz?usp=sharing

Observing the commands made in the last code, a new cell with code could be modified to consider the Shapiro-Wilk test.

import matplotlib.pyplot as plt

from scipy.stats import shapiro

# plotting all the means in one figure

k=0

fig, ax = plt.subplots(2, 2, figsize =(8, 8))

for i in range(0, 2):

  for j in range(0, 2):

    # Histogram for each x stored in means

    ax[i, j].hist(list_means_samples[k], 20, density = True)

    ax[i, j].set_title(label = 'Sample size = '+str(list_sample_size[k]))

    stat,p = shapiro(list_means_samples[k])

    print("The Test-Statistic and p-value are as follows:\nTest-Statistic = %.3f , p-value = %.3f"%(stat,p))

    k = k + 1

plt.show()

The Test-Statistic and p-value are as follows: Test-Statistic = 0.957 , p-value = 0.000 The Test-Statistic and p-value are as follows: Test-Statistic = 0.996 , p-value = 0.006 The Test-Statistic and p-value are as follows: Test-Statistic = 0.996 , p-value = 0.015 The Test-Statistic and p-value are as follows: Test-Statistic = 0.998 , p-value = 0.200