PST homework

Overview

Data file: case0202

Description: Anatomical abnormalities associated with schizophrenia

Tasks

1. Load the data file, find two observed data groups and separate them. Describe these two data groups. For each group find mean, variance and median.
2. For each group try to find probability density function (based on histogram) and distribution function (based on ecdf).
3. For each group find probability distribution.
   1. Approximate parameters of normal, exponential and uniform distribution.
   2. Add appropriate probability density functions (PDF) with estimated parameters to the histogram graphs.
   3. Discuss which of the distribution represents observed data the best.
4. For each group generate 100 random samples using distribution you chose as the most suitable, with parameters you estimated before. Compare histogram of simulated values with observed values.
5. For each group separately compute 95 % confidence interval for the mean.
6. For each group separately, with the 5% level of significance, test hypothesis whether the mean equals value of K (parameter of the task). You can use result of the previous task or output of a corresponding function in your software.
7. Test whether the observed groups have the same mean on the 5 % significance level. Specify types of tests and alternatives, so your choice suits the best the character of the investigated problem.