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Statistics 101
Chapter 10
Section 2
How to run a significance test
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Step 1: Identify the population of interest and the
parameter you want to draw conclusions about.
State the null and alternative hypothesis in words
and symbols.
Step 2: Choose the appropriate inference
procedure. Verify the conditions for using the
selected process.
Step 3: Carry out the inference procedure. Calculate
the test statistic and find the P-value.
Step 4: Interpret your results in the context of the
problem.
Tests of significance
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Confidence intervals – estimate a population
parameter
Tests of significance: assess the evidence
provided by data about some claim
concerning a population
An outcome that would rarely happen if a
claim were true is good evidence that the
claim is not true.
Reasoning of tests of
significance
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Null hypothesis: there is no effect or change
in the population H0 (H-nought)
Sweetness of colas:
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H0:μ = 0
Alternative Hypothesis: Ha is that the cola does lose
sweetness.
Ha: μ > 0
P - value
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Probability of a result at least as far out as
the result we actually got.
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Small P-values are evidence against H0
because they say that the observed result is
unlikely to occur just by chance.
How small is small enough to persuade us?
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0.05 is statistically significant.
Stating Hypotheses
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Null hypothesis.
Alternative hypothesis
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H0: μ = 0
Ha: μ > 0
This is called one-sided because we are
interested only in deviations from the null
hypothesis in one direction.
Two-sided
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Job Diagnosis Survey p 565
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H0: μ = 0
Ha: μ = 0
Statistical Significance
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If the P-value is as small or smaller than
alpha, we say that the data are statistically
significant at level alpha
Test for population mean
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Identify the population of interest and the
parameter
State the null and alternative hypothesis in
words and symbols
Choose the appropriate inference procedure
Calculate the test statistic
Find the P-value
Interpret your results
Z test for a population mean
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To test H0: μ = μ0 based on an SRS of size n
with unknown μ and known standard
deviation σ, compute one-sample z statistic
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Z = (x - μ0 ) / σ / √n
Tests with fixed significance
level
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Fail to reject instead of accept implies a
100% certainty in H0
Since 0.06 > 0.05 we fail to reject the H0.
There is not significance to conclude that the
students are less skilled.
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This is example 10.15
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Exercises
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10.27, 10.29 – 10.32, 10.33, 10.38, 10.40,
10.41, 10.45, 10.49, 10.56