4.1. Interval Estimates & Hypothesis Testing Flashcards
T-distribution…
Allows us to calculate interval estimates when the standard deviation is unknown.
Still uses a normal distribution for the population being sampled.
This can be applied in situations where the population deviates from normal.
This depends on the degrees of freedom.
As the number of degrees of freedom increases, the difference between the t-distribution and normal distribution becomes smaller.
When the underlying distribution is unknown…
We must rely on Central Limit Theorem.
This uses the standard normal distribution if it is known.
We can then use t-distribution if the standard distribution is not known.
A large sample size is preferable for such cases.
Hypothesis testing…
Used to test different theories about population parameters.
H1: alternative hypothesis.
H0: null hypothesis.
One- or two-tailed…
One-tailed: the values of the sample which cause rejection of the H0 fall in only one tail of the distribution (i.e. H0: mean = 5,000, H1: mean is smaller than 5,000).
Two-tailed: values of the sample can fall in either tail of the distribution to cause rejection of H0 (i.e. H0: mean = 5,000, H1: mean is greater or less than 5,000).
Errors in hypothesis testing…
Type I errors: we reject the H0 when we should accept it.
Type II errors: we accept the H0 when we should reject it.
Signifiance level…
The probability of rejecting H0 even when it is correct.
Confidence level = 1 - significance level.
So if the significance level is 0.05, this means we have a 5% chance of rejecting the H0 even when it is correct.
The confidence level in this case equals 95%.
Significance levels lead to types of errors…
The higher the significance level, the greater the risk of type I errors.
The lower the significance level, the greater the risk of type II errors.
P values…
P values are the probability that provides a measure of evidence against the null hypothesis.
Smaller P values indicate more evidence against the null hypothesis.
Instead of fixing a significance level before an event, it can be questioned what is the smallest significance level at which we would reject the null hypothesis.
Calculations…
Please see the Google Doc.
