Agriculture Reference
In-Depth Information
(e)
Selection of level of significance
: Depending
upon the objective of the study, type of param-
eter, type of study object, precision required,
etc., the appropriate level of significance is
required to be decided. Selection of suitable
level of significance (i.e., the region of rejec-
tion) is a must before the testing of hypothesis
actually takes place.
5. Test of equality of two population variances
from two normal populations with known
population means
6. Test of equality of two population variances
from two normal populations with unknown
population means
7. Test for equality of two population means
with known variances
8. Test for equality of two population means
with equal but unknown variance
9. Test for equality of two population means
with unequal and unknown variances—
Fisher-Berhans problem
10. Test equality of two population means under
the given condition of unknown population
variances from a bivariate normal population-
paired
Critical values
(f)
: Depending upon the type of
test (one sided or both sided), test statistic,
and its distribution, level of significance
values separating the zone of rejection and
the zone of acceptance are to be worked out
from the table of specific corresponding dis-
tribution. Critical region should be selected in
such a way that its power be maximum. A test
is significant (i.e., rejection of null hypo-
thesis) or not significant (acceptance of null
hypothesis) depending upon the values of the
calculated value of the test statistic and the
table value of the statistic at prefixed level of
significance. Fault in selection of the critical
values may lead to a wrong conclusion.
-test
11. Test for significance of population correla-
tion coefficient, that is,
t
H 0 :
ρ ¼
0 against
H 1 : ρ 6¼
0
12. Test for equality of two population variances
from a bivariate normal distribution
13. Test for specified values of intercept and
regression coefficient
(g)
Calculation of test statistic
: From the given
information, one needs to accurately calcu-
late the value of the test statistic under null
hypothesis.
in a simple linear
regression
14. Test for significance of the population multi-
ple correlation coefficient
15. Test for significance of population partial
correlation coefficient
The above tests are few to maintain but are
not exhaustive.
A. Tests Based on a Normal Population
Depending upon the type of test (i.e., one
sided or both sided) and the level of signifi-
cance, the limiting values of the critical
regions (i.e., region of acceptance and region
of rejection) under standard normal probabil-
ity curve are given as follows (Table 9.2 ):
(h)
Comparison
of calculated value of the statis-
tic at prefixed level of significance with that
of the corresponding table value.
Decision
(i)
with respect to rejection or accep-
tance of null hypothesis.
(j) Drawing conclusion in line with the questions
put forward in the objective of the study.
9.3
Statistical Test Based on
Normal Population
1. Test for specified value of population mean
with known population variance
2. Test for specified value of population mean
with unknown population variance
3. Test of significance for specified population
variance with known population mean (
Table 9.2
Critical values under
standard normal
probability curve
Level of
significance
α ¼ 0.05
Level of
significance
α ¼ 0.01
Type of test
)
4. Test of significance for specified popula-
tion variance with unknown population
mean (
μ
Both-sided test
1.960
2.576
1.645
2.330
One sided (left tailed)
One sided (right tailed)
1.645
2.330
μ
)
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