The rejection region will be
2
calc
z
z
. (Due to symmetry)
(d)
Conclusion
After we have computed the value of the test statistic using the sample data, we have to make
conclusion of our finding.
If the value of the test statistics
lies
in the critical region, we reject
0
H
. There is
sufficient evidence to
conclude that ………….(write
the statement of
1
H
in context) .
If the value of the test statistics
does not lie
in the critical region, we do not reject
0
H
.There is insufficient evidence to
say that ……(write
the statement of
1
H
in context).
Example 8.2 :
Experience has shown that the scores obtained in a particular test are normally distributed with mean
score 70 and variance 36. When the test is taken by a random sample of 36 students, the mean score is
68.5. Is there sufficient evidence, at 3% level, to conclude that these students have not performed as
well as expected?
Solution :
Let
X
denote the scores obtained by a randomly chosen student
Given
~ N(70,36)
X
,
n
36
T
o test
0
1
:
70
:
70
H
H
at 3% level of significance.
T
est Statistic:
Under
0
H
,
36
~ N 70,
36
X
and test
70
means that the
students
have
not
performed
as
well
as
expected.
0
z
Critical region
z
0
2
z
2
Critical region
Critical region
2
2
z
z

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