Module 1: Hypothesis Testing (t-tests) and Confidence Intervals
Introduction
In this module, we're going to build on the descriptive statistics concepts we've already learned about as we started to explore our data. This module will introduce the idea of a "hypothesis test" and how we implement one, specifically using the t-test and t-distributions. We'll also cover how to calculate p-values and use the results to interpret our hypothesis.
In addition, this module will cover one of the most important concepts in statistics: the Central Limit Theorem. We'll learn about the properties of sampling distributions and how to interpret the expected mean of a sample distribution, which will, in turn, lead to the idea of confidence intervals and how we know the confidence level of our results and predictions.
Learning Objectives
By the end of this module, you should be able to:
- Explain the purpose of a t-test and identify applications
- Set up and run a one-sample or two-sample t-test
- Set up and run a two-sample independent t-test
- Use a t-test p-value to draw a conclusion about the null and alternative hypothesis
- Explain the concepts of statistical estimate, precision, and standard error as they apply to inferential statistics
- Explain the implications of the Central Limit Theorem in inferential statistics
- Explain the purpose of and identify applications for confidence intervals
Guided Project
Project Resources
Open DS_121_ttests_confidence_intervals.ipynb in the GitHub repository below to follow along with the guided project:
GitHub: Hypothesis Tests and Confidence IntervalsKey Concepts
- Student's t-distribution and how it differs from normal distribution
- One-sample t-tests: comparing a sample mean to a known value
- Two-sample t-tests: comparing means between independent samples
- Calculating and interpreting t-values
- Understanding p-values in hypothesis testing
- The Central Limit Theorem and its significance in statistical inference
- Confidence intervals for estimating population parameters
Module Project
Project Tasks
In this module's project, you will be asked to:
- Formulate null and alternative hypotheses for given scenarios
- Perform one-sample and two-sample t-tests on real datasets
- Calculate and interpret p-values from t-tests
- Make conclusions about statistical significance based on hypothesis tests
- Calculate confidence intervals for population means
- Explain how the Central Limit Theorem applies to your analysis
Complete all tasks in the Jupyter notebook DS_121_hypothesis_confidence_Assignment_AG.ipynb provided in the GitHub repository.