Research Methodology - Dr. Krishan K. Pandey

Testing of Hypotheses I 189
Mathematically we can state:
Acceptance Region A: Z < 196 .
Rejection Region R : Z > 196 .
If the significance level is 5 per cent and the two-tailed test is to be applied, the probability of the
rejection area will be 0.05 (equally splitted on both tails of the curve as 0.025) and that of the
acceptance region will be 0.95 as shown in the above curve. If we take μ = 100 and if our sample
mean deviates significantly from 100 in either direction, then we shall reject the null hypothesis; but
if the sample mean does not deviate significantly from μ , in that case we shall accept the null
hypothesis.
But there are situations when only one-tailed test is considered appropriate. A one-tailed test
would be used when we are to test, say, whether the population mean is either lower than or higher
than some hypothesised value. For instance, if our H0 : μ = μHand
H
0 a: μ < μH
, then we are
0
interested in what is known as left-tailed test (wherein there is one rejection region only on the left
tail) which can be illustrated as below:
Rejection region
0.05 of area
Limit
Acceptance and rejection regions
in case of one tailed test (left-tail)
with 5% significance
Acceptance region
(Accept H0 if the sample
mean falls in this region)
0.45 of
area
Z = –1.645 H
0
Reject H0
if the sample mean
( X ) falls in this region
Fig. 9.2
0.50 of
area
Both taken together equals
0.95 or 95% of area
Mathematically we can state:
Acceptance Region A: Z >−1645 .
Rejection Region R: Z