Statistical Inference Project README

Overview

This repo contains my work from the course project from the Statistical Inference course from Johns Hopkins University within the Data Science Specialization on Coursera. The original instructions for the project can be found beneath the brief description section below. The scripts and markdowns were all created in RStudio.

Brief Description

As described in the original instructions below, the project consists of two parts. The files in this repo follow a naming convention that begins with C6_Project1 for Course 6 Project 1. The a or b following the 1 indicates either part a or part b of the project. Each part began with an R script to achieve the basic requirements of the project. The script was then used to help write an R markdown file. The markdowns were knit into html files using knitr (while retaining the intermediate md files). The course instructions asked to submit the assignment as a pdf, so the Rmd files were also knit to pdfs.

Original Project Instructions (abbreviated)

Credit for the material below goes to the original authors Caffo, Peng, and Leek from John Hopkins University. This material was accessed through the course content on Coursera.

The project consists of two parts:

• A simulation exercise.
• Basic inferential data analysis.

You will create a report to answer the questions. Given the nature of the series, ideally you'll use knitr to create the reports and convert to a pdf. (I will post a very simple introduction to knitr). However, feel free to use whatever software that you would like to create your pdf.

Each pdf report should be no more than 3 pages with 3 pages of supporting appendix material if needed (code, figures, etcetera).

Part 1: Simulation Exercise Instructions

In this project you will investigate the exponential distribution in R and compare it with the Central Limit Theorem. The exponential distribution can be simulated in R with rexp(n, lambda) where lambda is the rate parameter. The mean of exponential distribution is 1/lambda and the standard deviation is also 1/lambda. Set lambda = 0.2 for all of the simulations. You will investigate the distribution of averages of 40 exponentials. Note that you will need to do a thousand simulations.

Illustrate via simulation and associated explanatory text the properties of the distribution of the mean of 40 exponentials. You should:

• Show the sample mean and compare it to the theoretical mean of the distribution.
• Show how variable the sample is (via variance) and compare it to the theoretical variance of the distribution.
• Show that the distribution is approximately normal.

In point 3, focus on the difference between the distribution of a large collection of random exponentials and the distribution of a large collection of averages of 40 exponentials.

Part 2: Basic Inferential Data Analysis Instructions

Now in the second portion of the project, we're going to analyze the ToothGrowth data in the R datasets package.

• Load the ToothGrowth data and perform some basic exploratory data analyses
• Provide a basic summary of the data.
• Use confidence intervals and/or hypothesis tests to compare tooth growth by supp and dose. (Only use the techniques from class, even if there's other approaches worth considering)
• State your conclusions and the assumptions needed for your conclusions.