Hypothesis Test: in stats, we ask questions. We want to answer them with certainty.
Basic Logic of Hypothesis Testing
One sample mean test it is rarely done. You usually compare groups with it.
o For example: after 9/11 or earthquake in Japan, find population scores of
happiness/stress levels. You can’t study what happens before and after, so use
Theoretical values for μ (population mean) and s (sample standard deviation).
o Draw sample and deliver treatment. See what happens after. Then take mean of
sample for population.
Q: Did my treatment work? A: It didn’t work mean of sample is close to
mean of population OR It did work mean of sample is far from mean of
o Theoretical view: treat it as if you’re treating entire population.
o Example: researching depression in rats
μ=28.7 σ=7.6 M=50 After treatment: M=25.1
There are 2 possibilities: 1) The mean after treatment is smaller
because the therapy works. 2) By sampling error, I selected happy rats.
o Sampling Distribution
Outcome is unlikely under scenario that therapy didn’t work (region near tail
end of distribution)
Decision line usually appears at the last 5% in the tail end of the distribution.
Anything less that appears after the decision line is part of a rejected region.