Mathmatic Foundation of Test: week 3

ex 1

Chisq test is also a very popular test in psychometric, given that rchisq(1,1) is the R command to make an random draw for Chi-square distribution with df =1. Could we use the similar procedure about find what is 0.95 PR of this distribution?

ex 2

central limit theory

x <- rchisq(1000, 1)
hist(x, las = 1)

mean(x)

## [1] 0.9750786

var(x); sd(x)

## [1] 2.054334

## [1] 1.433295

sample distribution of chisq

times = 1000; sample.size = 36
df = k = 1
sample mean = mean(x) = k
sample variance = var(x) = 2k

mean and variance of sample distribution of chisq

## [1] 1.000912

## [1] 1.974101

ex 3

X = 3 * Z + 2

try try data

plot the dataset

just glimpse 2 * 2 for 4 plots

sample distribution of mean and variance