Statistical Inference Assignment 1

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

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. 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.

This exercise is asking you to use your knowledge of the theory given in class to relate the two distributions.

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.

Review criteria

• Did you show where the distribution is centered at and compare it to the theoretical center of the distribution?
• Did you show how variable it is and compare it to the theoretical variance of the distribution?
• Did you perform an exploratory data analysis of at least a single plot or table highlighting basic features of the data?
• Did the student perform some relevant confidence intervals and/or tests?
• Were the results of the tests and/or intervals interpreted in the context of the problem correctly?
• Did the student describe the assumptions needed for their conclusions?