So far, we've focused on summarizing the data directly in front of us using descriptive statistics. Now, we shift our attention to making informed inferences about a larger population based only on a smaller subset, or sample, of data. This is essential because accessing or analyzing an entire population (e.g., all potential customers, all sensor readings) is often impossible or too costly.

This chapter introduces the fundamental concepts of inferential statistics. You will learn how to:

• Distinguish between populations and samples and understand why sampling is necessary.
• Identify different sampling methods.
• Understand the Central Limit Theorem (CLT) and its crucial role in statistical inference, particularly regarding the distribution of sample means.
• Calculate point estimates for population parameters, such as using the sample mean $\bar{x}$ to estimate the population mean $\mu$.
• Construct and interpret confidence intervals, which provide a range of plausible values for a population parameter based on sample data.

We'll put these concepts into practice, using Python to simulate sampling distributions and compute estimates, bridging the gap between theory and application.