W1 L1 Inferential Statistics.

Aim of inferential statistics

Is to infer population parameters from sample statistics.

Two main concerns of inferential statistic

Estimation - Estimating a population parameter through the construction of a confidence interval
Hypothesis Testing - deciding whether to accept or reject a statement about a population parameter
That is, if the current result occurred by chance and is therefore a fluke or is an actual representation of a possible population

Explain this graph?

The shape of the sampling distribution - central limit theorem states that the 'sampling distribution of the mean tends towards a normal distribution as n increases, regardless of the shape of the population distribution'

Explain some properties of the sampling distribution of the mean?

Mean is - that is in the hypothetical sampling distribution - the mean of all the samples is the actual population mean. The sampling distribution of the mean’s variance can be influenced by only two things population variance and sample size n The sample distribution of the mean’s variance is known as a standard error of the mean

What is the effect of number of samples on sampling distribution?

The more accurate your sampling distribution - becomes narrower and will become more normal. ‘Tighter accuracy’ - the more the better.

What does the population standard deviation do to the sampling distribution?

Also influence the standard deviation of the sampling distribution - becomes narrower and more as the standard error decreases.

What is the typical sample size for the sample distribution of the mean to reach normal?

30

What are the typical symbols for Mean, Variance and Standard Deviation in statistics vs. parameters?