Week 7: Sampling Distribution, Point and Interval Estimators

Slides

Sampling Distribution

• Sampling distribution
• Distribution of a sample mean
• Central limit theorem
• Distribution of sample proportion

Point and Interval Estimators

• Point stimators
• Interval estimators

Performance Outcomes

You should feel confident to perform the following outcomes:

Sampling distribution

• Define and explain the concept of a sampling distribution and its role in statistics
• Describe the effect of sample size and the Central Limit Theorem on sampling distributions
• Calculate and interpret the mean and standard error of a sampling distribution
• Use sampling distributions to make inferences about population parameters
• Design and implement simulation studies to evaluate the performance and properties of statistical methods under various scenarios
• Use parametric simulation techniques to generate synthetic data and evaluate the performance of statistical methods under defined model assumptions

R programming (non-examinable)

• Create and use functions in R to encapsulate reusable code for performing specific tasks
• Apply functional programming concepts or for loops to perform repetitive tasks in programming

Point and interval estimators

• Define point estimators and explain their purpose in statistics
• Identify common point estimators for population parameters
• Describe the properties of good point estimators, such as unbiasedness and efficiency
• Define interval estimators and explain the concept of confidence intervals
• Interpret confidence intervals in the context of statistical inference
• Construct confidence intervals for population parameters using sample data
• Distinguish between point estimates and interval estimates in reporting results

Resources

If you don’t feel yet confident after going through the teaching materials or would like further resources, then you are also encouraged to go through the following materials.

• Statistical Inference via Data Science: A ModernDive into R and the Tidyverse (2nd Edition)
  • Chapter 7: Sampling
• R for Data Science (2nd Edition)
  • Chapter 25: Functions
  • Chapter 26: Iteration
• OpenIntro Statistics (4th Edition)
  • Chapter 5.1: Point estimates and sampling variability
  • Chapter 7.1.1 The distribution of \(\bar{x}\)
  • Chapter 7.1.2 Evaluating the two conditions required for modeling \(\bar{x}\)
  • Chapter 7.1.3 Introducing the \(t\)-distribution
• Statistical Inference via Data Science: A ModernDive into R and the Tidyverse (2nd Edition)
  • Chapter 8: Estimation, Confidence Intervals, and Bootstrapping
• OpenIntro Statistics (4th Edition)
  • Chapter 5.2: Confidence intervals for a proportion

This website, made using Quarto and hosted via GitHub Pages, is brought to you by the ANU Research School of Finance, Actuarial Studies and Statistics.