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. 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).
####Project Instructions, part One
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.
####Project Instructions, part Two
-
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.