Statistics 2
Table of Contents
- Discrete Random Variables
- The Poisson Distribution
- Central limit theorem for samples from a Poisson dist
- Poisson Approximating Binomial
- Continuous Random Variables
- Estimation
- t-distribution
- t vs normal
- Sampling Distribution of the Mean
- Hypothesis Testing
- Hypothesis testing for the mean of a Normal distribution
- Type I and Type II errors
- Chi Squared
Central limit theorem for samples from a Poisson dist
[b]1.[/b] Click to see the orginal distribution Poisson X with mean 4;[br][i]2.[/i] Click to see the distribution of the sample mean of X for different values of [i]n[/i];[br][i]3.[/i] Move the slider to see if the distribution of the sample mean is approximately normal.
Central limit theorem for samples from a Poisson dist
t-distribution
The red curve is the standard normal distribution with mean 0 and standard deviation 1. The blue curve is the t-distribution. Drag the slider to change the degrees of freedom.
Hypothesis testing for the mean of a Normal distribution
Choose the value of the mean for the null hypothesis, the form of the alternative hypothesis, the population standard deviation, and the sample size for the hypothesis test.[br][br]Press the New sample button to select a new sample of size n from a Normal population, with the given standard deviation and a mean which may or may not be the same as the mean in the null hypothesis.[br][br]The value of the test statistic is shown by the blue line, and the critical region is also shown on the graph.[br][br]Click the checkbox to show the true mean of the population from which the sample was taken. Was the test result correct?