Use Python to calculate confidence intervals

A confidence interval is a range of values used to estimate a population parameter, such as the mean or proportion, based on sample data. It provides a range within which we expect the true population parameter to lie, with a certain level of confidence. Confidence levels provide an estimate range that is more informative than a single point estimate. They give a sense of precision of the estimate and the uncertainty associated with sampling.

The key components of the confidence interval are:-

1. The sample statistic is a sample mean (x_bar) or sample proportion (p_hat) from the data.
2. The confidence level represents the probability that the confidence interval contains the true population parameter. Common confidence levels are 90%, 95%, and 99%.
3. The margin of error is the range above and below the sample statistic within which the population parameter is expected to lie.

In its most simplistic form, the confidence interval is calculated as:-

Confidence interval = sample statistic ∓ margin of error

The margin of error is calculated as:-