8.1: Hypothesis Testing
hypothesis testing process
1) Establish hypotheses to be tested. 2) Obtain a random sample from the population. 3) Assume the null hypothesis is true, analyze/examine sample data for contradictory evidence.
hypothesis test
A ___ is a procedure for testing a claim about a parameter of a population. A hypothesis test will always involve two hypotheses: null and alternative hypothesis.
do not reject
Otherwise, if the sample data do not strongly indicate the null hypothesis is false, we ___ the null hypothesis and do not conclude the alternative hypothesis is true. *FAILURE*
null hypothesis
The ___ (H0) is a statement that the value of a population parameter (such as proportion or mean) is equal to some claimed value. The statement will always have the form: Parameter = Value
alternative hypothesis
The ___ (H1) is the statement that the parameter has a value that somehow differs from the null hypothesis.
statistically significant
When we reject the null hypothesis at significance level α, we say the results are "___ ___ at level α".
the probability of a type II error.
denoted β.
small
ideally, both Type I and Type II errors should have ___ probabilities.
reject
if the sample data strongly indicate the statement of the null hypothesis is false, we ___ the null hypothesis and conclude the alternative hypothesis is true. *SUCCESS*
a hypothesis
is a claim or statement about a parameter of a population.
type II error
not rejecting the null hypothesis when it is in fact false.
null hypothesis
notated as H0
alternative hypothesis
notated as H1 (or sometimes Ha).
left tailed
parameter < value
right tailed
parameter > value
two tailed
parameter ≠ value
type I error
rejecting the null hypothesis when it is in fact true.
false
t or f: we always "accept" the null hypothesis.
true
t or f: we never say the defendant was proven innocent.
confidence interval ( interval estimate)
the ___ is built on the point estimate and contains the range of possible values for the unknown population parametereither the population proportion or mean.
significance level
the probability with which we are willing to risk a type I error. (α)
inferential statistics
used to make inferences or generalize an entire population using a sample. This includes the techniques of making decisions and drawing conclusions.
small, false, true
we use ___ significance levels because if we reject the null hypothesis, we want to be confident that the null hypothesis is ___ and the alternative is ___.
inversely related
α and β are ___ ___.
