Statistical Inference

This project consists of a Simulation Exercise as well as an Inferential Data Analysis of impact of Vitamin C on Tooth Development.

1. Simulation Exercise

In this first section, I 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. I investigate the distribution of averages of 40 exponentials. Note that they analysis includes thousand simulations.

I illustrate via simulation and associated explanatory text the properties of the distribution of the mean of 40 exponentials.

• Sample mean comparison it to the theoretical mean of the distribution.
• Variability of the sample (via variance) and comparison to the theoretical variance of the distribution.
• Demonstration that the distribution is approximately normal.

2. Inferential Data Analysis - Vitamin C Effect on Tooth Growth

Now in the second second, I analyze the effect of Vitamin C dosages and delivery methods on tooth development.