Critical Values
The critical values of t corresponding to three significance levels (1%, 5%, and 10%
level) and at 19 degrees of freedom is constructed using t distribution table, and the output is
given in the table:
Alpha
value
Degrees of
freedom
Table value of t – Right
tailed
Table value of t – left
tailed
α = 0.01
19
2.539

2.539
α = 0.05
19
1.729

1.729
α = 0.10
19
1.328

1.328
The computed test statistic (tvalue) is 1.23 with 38 degrees of freedom.
At the 1% significance
level, 2.43 is the critical value.
The significance of 5% has 1.69 is the critical value.
Finally,
10% significance has a critical value of 1.30.
From this, it is evident that as we increase the
significance level the range of acceptability for the Null hypothesis goes on decreasing. Hence,
we do not reject the null hypothesis.
Representing the above result in the form of a Number line would as below.
1%
5%
10%
t vlaue
__________________________________________________
2.539
1.729
1.328
0
1.23
As shown in the graph it is one tailed test and from the above data, for rejection to occur the
value for the corresponding level of significance must lie to the immediate left. It is evident that
the values obtained 1.23 clearly lies to the right of the rejection region be it 1%, 5% or 10%
significance level. Therefore, the null hypothesis is not rejected.
The enactment of the Sarbanes
Oxley Act did not significantly lower the average bank’s ROE than it was before the act.
Subscribe to view the full document.
HYPOTHESIS TESTING
7
tTest: TwoSample Assuming Equal Variances
For alpha =0.01
Before SOX
After SOX
Mean
30.632
21.422
Variance
811.6826274
307.292532
6
Observations
20
20
Pooled Variance
559.48758
Hypothesized Mean Difference
0
df
38
t Stat
1.23130149
P(T<=t) onetail
0.112888208
t Critical onetail
2.428567631
P(T<=t) twotail
0.225776415
t Critical twotail
2.711557602
The above result shows that there is a significant difference in the values of both the ROE
figures of the bank, i.e., before the introduction of the act and after the introduction of the act. It
is evident from the fact that T stat value is smaller than Tcritical value for one tail, so we accept
the Null hypothesis.
i.e. there is no significant difference between the two ROE’s and SOX did not lower the ROE
with any significance after the enactment of the act.
tTest: TwoSample Assuming Equal
Variances
For alpha =0.05
Before SOX
After SOX
Mean
30.632
21.422
Variance
811.6826274
307.292532
6
Observations
20
20
Pooled Variance
559.48758
Hypothesized Mean Difference
0
HYPOTHESIS TESTING
8
df
38
t Stat
1.23130149
P(T<=t) onetail
0.112888208
t Critical onetail
1.68595446
P(T<=t) twotail
0.225776415
t Critical twotail
2.024394164
The above result shows that there is a significant difference in the values of both the ROE figures
of the bank, i.e., before the introduction of the act and after the introduction of the act. It is
Subscribe to view the full document.
 Winter '18