Unbiased estimator for the population variance
Unbiased estimator for the population mean
Central Limit Theorem
Exam Questions – Estimation and sampling, Range
Type I error and Type II errors
Hypothesis test for the population mean
Confidence interval for a population proportion
Confidence interval for a population mean
Random sampling using random number tables or calculator
Difference between between a sample and a population
If X and Y have independent Poisson distributions then X + Y has a Poisson distribution
If X and Y have independent normal distributions then aX + bY has a normal distribution
If X has a normal distribution then so does aX + b
Var(aX + bY) = a2Var(X) + b2Var(Y)
E(aX + bY) = aE(X) + bE(Y)
What is a statistic?
In this video I take a sample from a population and look at the probability distribution of the sample mean.
Exam Questions – Normal approximation to the Poisson distribution
Exam Questions – Hypothesis tests: Poisson distribution
Exam Questions – Hypothesis tests: binomial distribution
Exam Questions – Estimation and sampling, Median
Exam Questions – Poisson approximation to the binomial distribution
Exam Questions – Probability density functions and cumulative distribution functions
Exam Questions – Poisson distribution
Two tailed test
Upper tail test
Lower tail test
Test for a Poisson mean
Two tailed test
Critical values – upper tail test
Critical values – lower tail test
Upper tail test
Lower tail test
Test for a binomial proportion
Sampling distribution of the mode and median
Following on from the distribution of the sample mean I now take a sample from a population and look at the probability distribution of the sample mode and sample median.
Sampling distribution of the sample mean
In this video I take a sample from a population and look at the probability distribution of the sample mean.
Simple random sampling
In this video I show you what we mean by a simple random sample, the conditions that must be true and the notation used.
The normal approximation to the Poisson distribution
In this video I show you how, under certain conditions a Poisson distribution can be approximated to a Normal distribution. You are also shown how to apply continuity corrections. Example