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Hypothesis Testing Hypothesis Testing Let‘s consider the American
justice system of ‗innocent until proven
guilty‘.
If we were to state this as a hypothesis, this would be:
H0 : The defendant is innocent.
H1 : The defendant is guilty. We make the initial assumption that the
defendant is innocent and
evidence at the trial (think sample data) either shows the claim of
guilt or it doesn‘t.
The evidence (sample data) will lead us to a verdict (conclusion). (
Business Statistics) Chapter 8 January 4, 2017 7 / 48 Introduction to
Hypothesis Testing Hypothesis Testing A hypothesis test is a five step
process.
1
2
3
4 5 State the hypotheses.
Calculate the test statistic (which is essentially a z-score)
Determine the p-value (we will discuss this in a moment).
Make a decision (where we side with either H0 or H1 ). To do this,
we
will need a significance level.
State a conclusion in terms of the problem. ( Business Statistics)
Chapter 8 January 4, 2017 8 / 48 Introduction to Hypothesis Testing
The p-value and Significance Level The p-value is the probability of
obtaining a test statistic as extreme
or more extreme than the one observed when we assume that H0 is
true.
We then compare the p-value to a significance level, denoted α, which
is similar to the confidence level for a confidence interval.
Typically, we set α = 0.05, which is equivalent to the concept of 95%
confidence intervals having a 95% success rate and a 5% failure rate.
( Business Statistics) Chapter 8 January 4, 2017 9 / 48 Introduction to
Hypothesis Testing The p-value and Significance Level In order to
make a conclusion about which hypothesis is more likely to
be correct, we have the following decision rule.
If p-value ≤ α, we declare the result significant and ‗reject H0 ‘.