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Unformatted text preview: umption When the conditions are met, we are ready to
find the confidence interval for the population
proportion, p. The confidence interval is phat +/- z* x SE(p-hat), where the standard
deviation of the proportion is estimated by SE
(p-hat) = rad(p-hat*q-hat/n) Don’t suggest that the parameter varies
Don’t claim that other samples will agree with
Don’t be certain about the parameter
Don’t forget: It’s about the parameter
Don’t claim to know too much
Do take responsibility
Do treat the whole interval equally ◦ Success/failure condition: We must expect at least
10 “successes” and 10 “failures” 4 10/30/2011 The null hypothesis which we denote H0,
specifies a population model parameter of
interest and proposes a value for that
Testing Hypothesis About
Proportions ◦ H0: parameter=hypothesized value The alternative hypothesis which we denote
HA, contains the values of the parameter
which we consider plausible if we reject the
◦ HA: parameter greater than, less then or simply not
equal to the hypothesized value Innocent until proven guilty
◦ Being innocent the null hypothesis Have to be proven guilty beyond a reasonable
◦ Look at the p-value If guilty, guilty beyond a reasonable doubt
◦ High enough -value Otherwise, not guilty. Never proven innocent!
◦ We never prove the null hypothesis true; rather, we
fail to reject it 1.
Conclusion We want to find the probability of seeing data
like this given the null hypothesis is true
◦ This probability is the P-value Never
Never accept the null hypothesis!
In computing a hypothesis test, we are
looking at the evidence to see if there the
probability of the null being “innocent” is so
low that it can’t possibly be true. Otherwise,
we concede it might be true First we state the null hypothesis
◦ Usually the skeptical claim that nothing’s different
Saying “oh yeah? Convince me?”
Have to pile up evidence to reject it
H0: parameter = hypothesized value The alternative hypothesis, HA , contains the
values of the parameter plausible when we
reject the null
The arriagnment 5 10/30/2011 Specify the model you will use to test the null
hypothesis and the parameter of interest
Different courts have different jurisdictions!
The test about proportions is called a oneoneproportion z-test
zCheck assumptions and conditions for using
model Actual calculation of our test statistic
Ultimate goal of the calculation is to obtain a
The trial The conclusion in a hypothesis test is always
a statement about the null hypothesis
The conclusion must state either that we
reject or that we fail to reject the null
hypothesis. And, it must be stated in context
The effect size matters! The conditions for the one-proportion z-test
are the same as for the one-proportion zinterval. We test the hypothesis H0: p=p0
using the statistic z= (p-hat-p0 / SD(p-hat)).
We use the hypothesized proportion to find
the standard deviation, SD (p-hat) =
When the conditions are met and the null
hypothesis is true, this statistic follows the
standard Normal model, so we can use that
model to obtain a P-value ◦ Think of confidence intervals! Questions?
Remember, Second Article due today! 6...
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This document was uploaded on 02/11/2014.
- Spring '14