Inferential stats and the sampling distribution

Question 1

Explain population for inferential statistics

Answer 1

Large group of observations to draw conclusions from
Real or hypothetical
Cannot be directly measured (large and unobtainable)

Question 2

Explain sample for inferential statistics

Answer 2

Subset of population
Draw conclusions about population

Question 3

Random sampling

Answer 3

Must be representative of the population

Contrast to bias sampling (Convenience sampling or snowball recruitment - A researcher identifies a small initial group of participants who meet the study criteria, then asks them to recommend others within their network who also fit the profile)

Question 4

Estimation

Answer 4

Sstimation of a population parameter (e.g. µ) through construct of a confidence interval

Question 5

Hypothesis testing

Answer 5

Deciding whether to accept or reject a statement about a population parameter

Question 6

Sampling distribution

Answer 6

It is a hypothetical distribution of values of a particular sample statistics formed by repeatedly drawing samples of n observations from population calculating the value of the statistic for each

Then could end up with a long list of M vales = create a frequency distribution

Question 7

Properties of sampling distribution of the mean

Answer 7

Normal distribution
Mean is µ (i.e. M is an unbiased estimator of µ)
Probability density curve
Symmetrical = unbiased estimator

Higer the sample the more accurate it would be for the population and the bell curve will be more narrow indicating little variance from the population mean

Question 8

Central limit theorem

Answer 8

Sampling distribution of mean tends towards a normal distributions as n increases, regardless of the shape of the population distribution

• as long as n is reasonably large, we can assume the sampling distribution is normal