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Formulating the Hypothesis
The null hypothesis is a statement
about the population value that will be
tested.
The null hypothesis will be rejected
only if the sample data provide
substantial contradictory evidence.
Formulating the Hypothesis
The alternative hypothesis is the
hypothesis that includes all population
values not covered by the null
hypothesis.
The alternative hypothesis is deemed to
be true if the null hypothesis is rejected.
Formulating the Hypothesis
The research hypothesis (usually the
alternative hypothesis):
Decision maker attempts to
demonstrate it to be true.
Deemed to be the most important to
the decision maker.
Not declared true unless the sample
data strongly indicates that it is true.
Types of Statistical Errors
Type I Error - This type of statistical
error occurs when the null hypothesis is
true and is rejected.
Type II Error - This type of statistical
error occurs when the null hypothesis is
false and is not rejected.
Types of Statistical Errors
State of Nature
Decision
Conclude Null True
(Don’t reject H00)
Conclude Null False
(Reject H00)
Null Hypothesis True
Null Hypothesis False
Correct Decision
Type II Error
Type I Error
Correct decision
Establishing the
Decision Rule
The critical value is
Determined by the significance level.
The cutoff value for a test statistic that
leads to either rejecting or not rejecting the
null hypothesis.
Establishing the
Decision Rule
The significance level is the maximum
probability of committing a Type I
statistical error. The probability is denoted
by the symbol .
Establishing the
Decision Rule
(Figure 8-3)
Sampling Distribution
Maximum probability
of committing a Type I
error = 
Do not reject H0
  25
x
Reject H0
x
Establishing the Critical
Value as a z -Value
From the standard normal table
z  0.10  1.28
Rejection region
 = 0.10
Then
z  1.28
0.5
0.4
0
  25
z  1.28
z
Establishing the
Decision Rule
The test statistic is a function of the
sampled observations that provides
a basis for testing a statistical
hypothesis.
Test Statistic in the
Rejection Region
Rejection region
 = 0.10
0.5
0.4
0
z  1.28
z  2.69
z
Establishing the
Decision Rule
The p-value is
The probability of obtaining a test
statistic at least as extreme as the test
statistic we calculated from the sample.
Also known as the observed significance
level.
Relationship Between the pValue and the Rejection Region
Rejection region
 = 0.10
p-value = 0.0036
0.5
0.4
0
z  1.28
z  2.69
z
Using the p-Value to Conduct
the Hypothesis Test
If the p-value is less than or equal to a,
reject the null hypothesis.
If the p-value is greater than a, do not
reject the null hypothesis.
Example:
For  = 0.05 with the p-value = 0.02 for a
particular test, then the null hypothesis is
rejected.
One-Tailed Hypothesis Tests
A one-tailed hypothesis test is a
test in which the entire rejection
region is located in one tail of the
test statistic’s distribution.
Two-Tailed Hypothesis Tests
A two-tailed hypothesis test is a
test in which the rejection region
is split between the two tails of
the test statistic’s distribution.
Two-Tailed Hypothesis Tests
(Figure 8-7)

 0.05
2

 0.05
2
z  1.645
0
z  1.645
z
When s Is Unknown
The sample standard deviation is
used.
The test statistic is calculated as
x


t s
n
The critical value is found from
the t-table (Appendix F) using n-1
degrees of freedom.