Research Methodology - Dr. Krishan K. Pandey

190 Research Methodology
If our μ = 100 and if our sample mean deviates significantly from100 in the lower direction, we
shall reject H , otherwise we shall accept H at a certain level of significance. If the significance
0 0
level in the given case is kept at 5%, then the rejection region will be equal to 0.05 of area in the left
tail as has been shown in the above curve.
In case our H0 : μ = μHand
H
0 a: μ > μH
, we are then interested in what is known as one-
0
tailed test (right tail) and the rejection region will be on the right tail of the curve as shown below:
Acceptance and rejection regions
in case of one-tailed test (right tail)
with 5% significance level
Acceptance region
(Accept H0 if the sample
mean falls in this region)
0.05 of area 0.45 of area
Both taken together equals
0.95 or 95% of area
H
0
Fig. 9.3
Rejection region
0.05 of area
Mathematically we can state:
Acceptance Region A: Z < 1645 .
Rejection Region A: Z > 1645 .
If our μ = 100 and if our sample mean deviates significantly from 100 in the upward direction, we
shall reject H , otherwise we shall accept the same. If in the given case the significance level is kept
0
at 5%, then the rejection region will be equal to 0.05 of area in the right-tail as has been shown in the
above curve.
It should always be remembered that accepting H on the basis of sample information does not
0
constitute the proof that H is true. We only mean that there is no statistical evidence to reject it, but
0
we are certainly not saying that H is true (although we behave as if H is true).
0 0
Limit
Z = –1.645
Reject H0 if the sample mean
falls in this region