Sample evidence is insufficient to reject g1834 g2868

sample evidence is insufficient to reject g1834
g2868
at g2009g3404.05 . Since
the null hypothesis is the “status-quo” hypothesis, the effect of
not rejecting g1834
g2868
is to maintain the status quo.

The Elements of a Test of Hypothesis
The table above summarizes the 4 possible outcomes of a test
of hypothesis. Note that a Type I error can be made only when
the null hypothesis is rejected and a Type II error can be made
only when the null hypothesis is accepted.
Conclusion g2164
g2777
true g2164
g2183
true
Accept g1834
g2868
Correct decision Type II error (probability g2010 )
Reject g1834
g2868
Type I error (probability g2009 ) Correct decision

The Elements of a Test of Hypothesis
• Our policy will be to make a decision only when we know the
probability of making the error that corresponds to that
decision
• Because g2009 is usually specified by the analyst, we will
generally be able to reject g1834
g2868
when the sample evidence
supports that decision.
• However, since g2010 is usually not specified, we will generally
avoid the decision to accept g1834
g2868
, preferring instead to state
that the sample evidence is insufficient to reject g1834
g2868
when the
test statistic is not in the rejection region

The Elements of a Test of Hypothesis
• The elements of a test of hypothesis are summarized as
follows (note that the first 4 must be specified before the
experiment is performed):
1. Null hypothesis ( g1834
g2868
): A theory about the specific values of one or
more population parameters. The theory generally represents the
status quo, which we adopt until it is proven false. The theory is
stated as g1834
g2868
: parameter=value
2. Alternative hypothesis ( g1834
g3028
): A theory that contradicts the null
hypothesis. The theory generally represents that which we will adopt
only when sufficient evidence exists to support it.

The Elements of a Test of Hypothesis
• The elements of a test of hypothesis are summarized as
follows (note that the first 4 must be specified before the
experiment is performed):
3. Test statistic: A sample statistic used to decide whether to reject the
null hypothesis.
4. Rejection region: The numerical values of the test statistic for which
the null hypothesis will be rejected. The rejection region is chosen so
that the probability is g2009 that it will contain the test statistic when the
null hypothesis is true . The value of g2009 is usually chosen to be small
and is referred to as the level of significance of the test

The Elements of a Test of Hypothesis
• The elements of a test of hypothesis are summarized as
follows:
5. Assumptions: Clear statements of any assumptions made about the
population being sampled.
6. Experiment and calculation of test statistic: Performance of the
sampling experiment and determination of the numerical value of the
test statistic.

The Elements of a Test of Hypothesis
• The elements of a test of hypothesis are summarized as
follows:
7. Conclusion:
a. If the numerical value of the test statistic falls in the rejection region, we
reject the null hypothesis. We know that the hypothesis-testing process
will lead to this conclusion (Type I error) 100α% of the time