Ch 14 - Introduction to Inference Flashcards
Significance tests
Someone makes a claim about the unknown value of
a population parameter
We check whether or not this claim makes sense in light of the “evidence” gathered (sample data).
A test of statistical significance tests
a specific hypothesis using sample data to decide on the validity of the hypothesis.
null vs alternative hypothesis
One-sided vs. two-sided alternatives
What determines the choice of a one-sided versus two-sided test is
1) the question we are asking and
2) what we know about the problem before performing the test.
If the question or problem is asymmetric, then Ha should be one-sided. If not, Ha should be two-sided.
P-value:
The probability, if H0 were true, of
- obtaining a sample statistic as extreme as the one obtained or more extreme in the direction of Ha.
small vs large p value
P-values are probabilities, so they are always
a number between 0 and 1
area under curve (of extremes)
The order of magnitude of the P-value matters more than
its exact numerical value.
The significance level, α, is the
largest P-value tolerated for rejecting H0 (how much evidence against H0 we require).
This value is decided arbitrarily before conducting the test - it is a part of designing the test
When the significance level, α, is ___ reject Ho
To test H0: µ = µ0 using a random sample of size n from a Normal population with known standard deviation σ, we use the
null sampling distribution N(µ0, σ√n).
The P-value is the area under N(µ0, σ√n) for values
of x̅ at least as extreme in the direction of Ha as that of our random sample
To calculate the P-value for a two-sided test, use
the symmetry of the normal curve. Find the P-value for a one-sided test and double it.
Because a two-sided test is symmetric, you can easily use a confidence interval to test a two-sided hypothesis.
In a two-sided test,
C=
A sample gives a 99% confidence interval of 0.83 - 0.85
With 99% confidence, could samples be from populations with µ =0.86? µ =0.85?
A confidence interval gives a black and white answer: ____ But it also estimates a ____
Reject or don’t reject H0.
range of likely values for the true population mean µ.
99% sure true mean lies in interval
A P-value quantifies how strong the evidence is against the H0. But if you reject H0, it ____
doesn’t provide any information about the true population mean µ.
confidence interval vs test of significance
