Inferential statistics and Hypothesis Testing
Inferential statistics allows us to draw conclusions about populations based on sample data, enabling us to make predictions and test theories about the broader world using limited information.
Understanding Statistical Inference
Statistical inference is the process of using data from a sample to make estimates and test hypotheses about a population. While descriptive statistics summarizes what's in your data, inferential statistics helps you reach conclusions that extend beyond the immediate data.
The fundamental concept behind inferential statistics is that we rarely have access to data from an entire population (e.g., all voters in a country, all patients with a certain condition). Instead, we collect data from a representative sample and use mathematical principles to make inferences about the whole population.
- The sample must be representative of the population
- The sample must be sufficiently large
Confidence Intervals
A confidence interval provides a range of values that likely contains the unknown population parameter with a specified level of confidence.
For example, instead of estimating that the mean height of all 18-year-old males is exactly 175 cm (a point estimate), we might say that we are 95% confident that the mean height is between 173.5 cm and 176.5 cm (an interval estimate).
The formula for a confidence interval for a population mean when the population standard deviation is known is: