# Inferential Statistics

### Prerequisites

• Knowledge of basic probability theory (random variables, probability distributions)
• Basic calculus

### Course Outcomes

After completing this course, the student should be familiar with the basic concepts and methods of inferential statistics. The student should understand the differences between populations and samples, and how sample data can be used to make inferences about a population. The student should know how to estimate some basic distribution parameters using either the maximum likelihood method, of the method of moments. The student should also know how to perform tests of hypothesis concerning population means, variances, and proportions, as well as how to determine the sample size required for a certain level of statistical confidence.

### Why learn Inferential Statistics?

To ensure that your project will work as intended, you will have to perform a wide variety of tests on your payload and its components. Questions such as “which component is better for our purposes, A or B?”, “will component A last as long as we need it to last for a successful mission?” or “How many components do we expect will fail during our mission?” are all important questions that can only be answered through experimentation. However, the results provided by your experiments will have some degree of uncertainty. For example, suppose you perform some tests on the reliability of five components of type A and five components of type B, and your results indicate that component A, on average, is more reliable than component B. Given that you have not (and cannot) tested all components of type A and all components of type B that exist, you can only cautiously claim that A is better. You cannot affirm this with absolute certainty. How, then, can you trust your results if they are uncertain? Inferential statistics allows you to design and analyze your experiments and their outcome so that you can reach conclusions with a certain degree of confidence, even under conditions of uncertainty.

### Syllabus

1. What is Inferential Statistics?
2. Foundations of Inferential Statistics
3. Estimators and Estimates
4. Maximum Likelihood Estimation
5. Method of Moments
6. What is Hypothesis Testing?
7. Types of Error
8. Procedure for Testing Hypotheses
9. Hypotheses Tests for:
• The mean of a population
• The difference of the means of two populations
• The variance of a population
• The ratio of two variances
• Paired observations
• One proportion
• The difference between two proportions
• More than two proportions