Critical Values The critical values of t corresponding to three significance

Critical values the critical values of t

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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 (t-value) 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.
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HYPOTHESIS TESTING 7 t-Test: Two-Sample 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) one-tail 0.112888208 t Critical one-tail 2.428567631 P(T<=t) two-tail 0.225776415 t Critical two-tail 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 T-critical 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. t-Test: Two-Sample 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
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HYPOTHESIS TESTING 8 df 38 t Stat 1.23130149 P(T<=t) one-tail 0.112888208 t Critical one-tail 1.68595446 P(T<=t) two-tail 0.225776415 t Critical two-tail 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
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