Statistical Significance

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Statistical Significance
The power of ALPHA
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The decisive value of P is called the
significance level. We write it as a, the Greek
letter alpha.
Significant in the statistical sense does not
mean important. It means simply not likely to
happen just by chance.
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Statistical Significance If the P-value is as
small as or smaller than alpha, we say that the
data are statistically significant at level a.
In practice, the most commonly used significance
level is a 0.05
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To test the hypothesis H0 µ µ0 based on an SRS
of size n from a population with unknown mean µ
and known standard deviation s, compute the
one-sample z statistic
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Step 1 Hypotheses Identify the population of
interest and the parameter you want to draw
conclusions about. State hypotheses.
Step 2 Conditions Choose the appropriate
inference procedure. Verify the conditions for
using it.

• Step 3 Calculations If the conditions are met,
  carry out the inference procedure.
• Calculate the test statistic.Find the P-value.

• Step 4 Interpretation Interpret your results in
  the context of the problem.
• Interpret the P-value or make a decision about H0
  using statistical significance.
• Don't forget the 3 C's conclusion, connection,
  and context.

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reject H0 or fail
to reject H0
we will reject H0 if our result is statistically
significant at the given a level.
That is, we will fail to reject H0 if our result
is not significant at the given a level.
EXAMPLE
Ho µ 0, there is NO difference in job
satisfaction between the two work environments
Ho µ ? 0, there is a difference in job
satisfaction between the two work environments
a .05
p .0234
Therefore, our hypothesis testing for this
particular case is statistically significant at
a .05
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A certain random number generator is supposed to
produce random numbers that are uniformly
distributed on the interval from 0 to 1. If this
is true, the numbers generated come from a
population with µ 0.5 and s 0.2887. A command
to generate 100 random numbers gives outcomes
with mean x 0.4365. Assume that the population
s remains fixed. We want to test H0 µ 0.5
versus Ha µ ? 0.5. (a) Calculate the value of
the z test statistic and the P-value. (b) Is the
result significant at the 5 level (a 0.05)?
Why or why not? (c) Is the result significant at
the 1 level (a 0.01)? Why or why not? (d) What
decision would you make about H0 in part (b)?
Part (c)? Explain.
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(a) Calculate the value of the z test statistic
and the P-value. (b) Is the result significant
at the 5 level (a 0.05)? Why or why not? (c)
Is the result significant at the 1 level (a
0.01)? Why or why not?
Since the P-value is less than 0.05, we say that
the result is statistically significant at the 5
level.
Since the P-value is greater than 0.01, we say
that the result is not statistically significant
at the 1 level.
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(d) What decision would you make about H0 in part
(b)? Part (c)? Explain.
At the 5 level, we would reject Ho and conclude
that the random number generator does not produce
numbers with an average of 0.5. At the 1
level, we would not reject Ho and conclude that
the observed deviation from the mean of 0.5 is
something that could happen by chance. That is,
we would conclude that the random number
generator is working fine at the 1 level