How to Calculate Confidence Intervals in Python?

To calculate confidence intervals in Python, you can use the scipy.stats library. The library provides functions to calculate confidence intervals for both the normal and t-distributions.

Here’s an example of how to calculate a 95% confidence interval for a normally distributed set of data:

import numpy as np
from scipy import stats

# Generate some example data
data = np.random.normal(size=100)

# Calculate the mean and standard deviation of the data
mean = np.mean(data)
std = np.std(data, ddof=1)

# Calculate the 95% confidence interval
n = len(data)
se = std / np.sqrt(n)
z = stats.norm.ppf(0.975)
ci = (mean - z * se, mean + z * se)

print("Sample mean:", mean)
print("Standard deviation:", std)
print("95% Confidence interval:", ci)

In this example, we first generate some example data using numpy.random.normal(). We then calculate the sample mean and standard deviation of the data using numpy.mean() and numpy.std(). To calculate the 95% confidence interval, we first calculate the standard error of the mean using std / np.sqrt(n), where n is the sample size. We then calculate the z-score for a 95% confidence interval using stats.norm.ppf(0.975). Finally, we calculate the confidence interval using (mean - z * se, mean + z * se).

You can use the stats.t functions in a similar way to calculate confidence intervals for t-distributions.