The following function performs a paired t-test.
```python
ttest_rel(a, b, alternative='two-sided')
```
It is similar to the one for independent samples, but here we do not obligate to check the homogeneity of variance. Paired t-test **does not** assume that variances are equal.  
To perform a paired t-test, samples' **sizes must be equal**.

Knowing this, you can move to the task where you will perform a paired t-test. 

Here you have data about the number of downloading one app; look at the samples: the mean values are almost equal.

import pandas as pd
import matplotlib.pyplot as plt

# Read the data
before = pd.read_csv('https://codefinity-content-media.s3.eu-west-1.amazonaws.com/a849660e-ddfa-4033-80a6-94a1b7772e23/Testing2.0/before.csv').squeeze()
after = pd.read_csv('https://codefinity-content-media.s3.eu-west-1.amazonaws.com/a849660e-ddfa-4033-80a6-94a1b7772e23/Testing2.0/after.csv').squeeze()
# Plot histograms
plt.hist(before, alpha=0.7)
plt.hist(after, alpha=0.7)
# Plot the means
plt.axvline(before.mean(), color='blue', linestyle='dashed')
plt.axvline(after.mean(), color='gold', linestyle='dashed')

This section will help us deal with the first real statistical case: finding confidence intervals. It requires knowledge of NumPy, pandas, Matplotlib, and Seaborn library to calculate math formulas and build visualization! To encourage you to pass this section, I want to point out that you will run across a small amount of theory but a significant amount of practice!

An inseparable part of a data analyst's life is conducting hypothesis testing. After completing this section, you will understand the idea behind testing in statistics and will be able to conduct a t-test using Python.

Learning Statistics with Python

Paired t-test

Task