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Significance Tests: The Basics
Section 11.1
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What is a Significance Test?
A formal procedure for comparing observeddata with a hypothesis whose truth we want toassess.
The hypothesis is a statement about apopulation parameter.
The results of a test are expressed in terms of aprobability that measures how well the data
and the hypothesis agree.The reasoning of hypothesis tests, like that of
confidence intervals, is based on asking whatwould happen if we repeated the experiment or
sampling procedure many, many times.
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Stating Hypotheses
Notation:
the null hypothesis: H0
the alternative hypothesis: Ha
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Can You Please Hurry It Up?
Vehicle accidents can result in serious injuries to driversand passengers. When they do, someone usually calls 911.Police, firefighters, and paramedics respond to theseemergency calls as quickly as possible. Slow response times
can have serious consequences for accident victims. In caseof life-threatening injuries, victims generally need medicalattention within 8 minutes of the crash. Several cities havebegun to monitor paramedic response times. In one suchcity, the mean response time to all accidents involving life-threatening injuries last year was = 6.7 minutes with a
standard deviation of 2 minutes. The city manager sharesthis information with emergency personnel and encouragesthem to do better next year. At the end of the followingyear, the city manager selects an SRS of 400 calls involvinglife-threatening injuries and examines the response times.The sample mean was 6.48 minutes. Do these data provide
good evidence that response times have decreased sincelast year?
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If response times have not decreased, the mean response
time for 400 calls will have this sampling distribution. If the
result had been 6.61 minutes, that could easily happen just
by chance. But our results was so far out in the tail that it is
good evidence of a decrease in response times.
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One Sided or Two ?
It that situation, we are seeking evidence of a
decrease in response time this year. The null
hypothesis would be that there is no decrease
and the alternative would be that there is adecrease.
H0: = 6.7 minutes
Ha: < 6.7 minutes
This is an example of a one-sided test because
we are interested only in deviations from the
null hypothesis in one direction.
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If Youre Happy and You Know It
Does the job satisfaction of assembly workersdiffer when their work is machine-paced ratherthan self-paced? One study chose 18 subjects atrandom from a group of people who assembledelectronic devices. Half of the subjects wereassigned at random to each of two groups. Bothgroups did similar assembly work but one worksetup allowed workers to pace themselves, and
the other featured an assembly line that movedat fixed time intervals so that the workers werepaced by machine. After two weeks, all subjectstook the Job Diagnosis Survey, a test of jobsatisfaction. Then they switched work setups and
took the JDS again after two more weeks.
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One Sided or Two ?
It that situation, we are seeking evidence
of a difference in JDS scores in the
population of all assembly workers.
H0: = 0
Ha: 0
This is an example of a two-sided test
because the direction of the difference
was not specified.
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Some Cautions!
Hypotheses always refer to some population,
not to a particular outcome, so always state
the hypotheses in terms of the population
parameter, not the sample statistic.
The alternative hypothesis should express the
hopes or suspicions we have before we see thedata. It is cheating to first look at the data and
then create you hypotheses based n what the
data show.
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Components of a Hypothesis Test For a
Population Mean (with known)
1. Name the procedure:
A hypothesis test for a population
mean ( known)
2. State the hypotheses and define any
symbols used:
H0: = _________
Ha: , or _________
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3. Check the conditions:
S SRS from the population of
interest
I observations are independent
(N> 10n)
N population distribution is ~Northe sample size is large enough
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4. Do the math:
Calculate the test statistic and find theassociated probability:
Is it always good to include a sketchthat illustrates the situation.
0 0( , , | | ) _____ x x
z P z or z
n n
Q Q
W W
! " !
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P for Probability!
A P-value:
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What Did You Just Say to Me?
This test (is/is not) statistically
significant since the P-value, ____, is
(>/
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Statistical Significance
Significant in the
statistical sense does
not mean important.
It means simply not
likely to happen just
by chance.