Exploring the Central Limit Theorem through Simulation and Inferential Analysis of Tooth Growth

Overview

This report investigates the exponential distribution using simulation and compares it to theoretical values, illustrating the Central Limit Theorem (CLT). It also analyzes the ToothGrowth dataset using exploratory data analysis and statistical inference.

Global chunk options

knitr::opts_chunk$set(echo = TRUE, message = TRUE, warning = TRUE, fig.width = 6, fig.height = 4, dpi = 96) set.seed(123) # reproducibility

Part 1: Simulation of Exponential Distribution

We simulate averages of 40 exponential random variables with rate parameter 𝜆 = 0.2 λ=0.2.

Theoretical mean: 1 / 𝜆 = 5 1/λ=5

Theoretical variance of sample mean: ( 1 / 𝜆 ) 2 / 40 = 0.625 (1/λ) 2 /40=0.625 Sample Mean vs Theoretical Mean

Sample Variance vs Theoretical Variance Normality Check