# Data Science Foundations: Statistical Inference

Data Science Foundations: Statistical Inference is a comprehensive program designed to provide learners with a strong understanding of probability theory and statistical inference in preparation for delving into the broader study of statistics. Through this course, participants will gain the essential skills required to perform fundamental statistical analysis of a data set using the R programming language.

The course comprises three modules, each covering key aspects of statistical inference. Module 1 focuses on probability theory, emphasizing its importance in statistics and data science, along with the relationship between conditional and independent events. Module 2 delves into statistical inference for estimation, teaching learners to identify characteristics of "good" estimators and construct and interpret confidence intervals. Module 3 explores statistical inference and hypothesis testing in data science applications, covering topics such as composite hypothesis, test statistics, and sampling distributions.

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##### Course Modules

This course consists of three modules. Module 1 covers probability theory, Module 2 focuses on statistical inference for estimation, and Module 3 explores statistical inference and hypothesis testing in data science applications.

#### Probability Theory: Foundation for Data Science

Module 1: Probability Theory: Foundation for Data Science

• Explain the importance of probability in statistics and data science.
• Explore the relationship between conditional and independent events in a statistical experiment.
• Calculate the expectation and variance of random variables and develop intuition in probability theory.

#### Statistical Inference for Estimation in Data Science

Module 2: Statistical Inference for Estimation in Data Science

• Identify characteristics of "good" estimators and compare competing estimators.
• Construct sound estimators using maximum likelihood and method of moments estimation techniques.
• Construct and interpret confidence intervals for one and two population means, proportions, and a population variance.

#### Statistical Inference and Hypothesis Testing in Data Science Applications

Module 3: Statistical Inference and Hypothesis Testing in Data Science Applications

• Define a composite hypothesis and the level of significance for a test with a composite null hypothesis.
• Define a test statistic, level of significance, and the rejection region for a hypothesis test.
• Perform tests concerning a true population variance and compute the sampling distributions for the sample mean and sample minimum of the exponential distribution.

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