School

Concordia University **We aren't endorsed by this school

Course

COMP 233

Subject

Statistics

Date

Aug 13, 2023

Pages

29

Uploaded by NadineMohamed on coursehero.com

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HYPOTHESIS
TESTING

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DEF.: Hypothesis Testing;
Hypothesis Testing
is a Statistical test used to determine whether the
hypothesis assumed for a random sample of data, stands true for the
entire population. Simply, the hypothesis is an assumption which is
tested to determine the relationship between two data sets (sample
and population).
In Hypothesis Testing, two opposing hypotheses about a population are
formed:
Null Hypothesis (H
0
)
and
Alternative Hypothesis (H
a
)
.
The Null Hypothesis is the statement which asserts there is no
difference between the sample Statistic and population parameter; and
is the one which is tested, while the Alternative Hypothesis is the
statement which stands true if the Null Hypothesis is rejected.
The following
Hypothesis Testing Procedure
is followed to test the
assumption made:
1.
Set up a Hypothesis Test:
Formulate the Null, and Alternate Hypothesis.
2.
Set a suitable Significance Level.
3.
Determine a suitable Test Statistic.
4.
Determine the Critical Region.
5.
Perform computations.
6.
Formulate a reject/accept Null Hypothesis decision.

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While testing the hypothesis, an individual may commit the following
types of error:
1.
Type-I Error:
True Null Hypothesis is rejected, i.e. Null Hypothesis is
rejected when it should be accepted. The probability of committing a
type-I error is denoted by
α
,
and is called the level of significance.
If
α =
P[type-
I error] = P[reject H
0
⃒
H
0
is true]
then (1
−
α) =
P[accept H
0
⃒
H
0
is true].
(1
−
α) corresponds to the concept of
Confidence Interval
.
2.
Type-II Error:
A False Null Hypothesis is accepted, i.e. Null Hypothesis is
accepted when it should be rejected. The probability of committing a
type-II error is denoted by
β.
If
β =
P[type-
II error] = P[accept H
0
⃒
H
0
is false]
then (1
−
β) =
P[reject H
o
⃒
H
0
is false].
(1
−
β)
is defined as the
Power of a Statistical Test.

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