W6 Lectures t-distribution; confidence intervals and estimation + iNZight + degrees of freedom Flashcards
t-distributions
based on the standard Normal distribution and are used with continuous variables
t-distribution gets closer to the standard Normal distribution when?
the sample size increases - most identical results are present
what is a point estimate?
is the mean/median taken from the sample data that estimates the population’s true mean/median
what is an interval estimate?
A confidence interval is a range of values that likely includes the true average (mean) or middle value (median) of a population.
The interval’s size depends on data variation, sample size, and confidence level.
what is a margin of error
The margin of error shows how much the sample results might differ from the true average (mean) of the whole population.
how do you get the bounds or limits
point estimate +/- margin of error
t-tests characteristics
to test whether a population mean is equal to a particular (hypothesised) value.
- based on the Normal distribution
- uses the point estimate of the population mean
what is the value of the mean of a t-distribution
0
how do you calculate the t-statistic
sample mean
sample standard deviation
sample size
t= x-bar - u/ s/root(n)
t-test hypotheses
H0: u = u0
H1: u > u0 or H1: u < u0 or H1: u =/ u0
Definition of degrees of freedom
Degrees of freedom (df) can be defined as ‘the number of observations in the calculation of a statistic that are free to vary’
Definition of Formal inference
to make objective inference from something that is just a sample to a whole population
