Research Question 4.448613 Calculate the return on equity (ROE) for a sample of

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Research Question

4.448613

Calculate the return on equity (ROE) for a sample of 20 banks for the year before the Sarbanes-Oxley Act was enacted. For the same sample of banks, calculate the ROE for the year following the enactment of the Sarbanes-Oxley Act.

Later, answer the following questions:

After the enactment of the Sarbanes-Oxley Act, was the average bank’s ROE lower than it was before the act? If so, why do you think that was the case?

What is the null hypothesis for this hypothesis test?

What is the alternative hypothesis for this hypothesis test?

Choose at least three different significant levels to conduct the hypothesis test. Is it possible that a Type I error occurred with the hypothesis test? Why or why not?

Is it possible that a Type II error occurred? Why or why not?

Name City State ROE 2001 ROE 2003 Difference United Heritage Bank Orlando FL 4.653617 4.243418 -0.410199 1st Bank Oklahoma Claremore OK 16.62094 16.94447 0.32353 1st Bank of Troy Troy KS 4.653617 4.243418 -0.410199 1st Choice Bank Houston TX 11.38230695 14.72548 3.343173 1st Bank Yuma Yuma AZ -22.9336 5.38686 28.32046 Almance National Graham NC -3.7884 7.850242 11.638642 Alabama Exchange Tuskegee AL 19.20605 17.30685 1.8992 Alabama Trust Bank Sylacauga AL 1.128313 9.646935 8.518622 First Credit Bank Los Angeles CA 16.17493 22.84361 6.66868 Alamo Bank Alamo TX 13.99432 14.61002 0.6157 Alamerica Bank Birmingham AL 4.362714 8.311734 3.94902 First Crawford State Robinson IL 14.58462 13.08854 -1.49608 Palm Desert National Palm Desert CA 18.58533 16.50701 -2.07832 Palmetto State Bank Hampton SC 16.03645 15.52283 -0.51362 First Dakota National Yankton SD 10.61072 7.698127 -2.912593 First Dupage Bank Westmont IL -12.5312 5.107998 17.639198 First Delta Bank Marked Tree AR 8.405722 4.669861 -3.735861 Palm Beach County Boynton Beach FL 5.752188 16.0989 10.346712 Palmer Bank Taylorville IL -3.37784 6.907977 10.285817 Palmyra State Bank Palmyra MO -3.11141 1.337203

4.448613

Explanation / Answer

The average return on equity (ROE) for a sample of 20 banks for the year before the Sarbanes-Oxley Act is given as 6.020469.

The average return on equity (ROE) for a sample of 20 banks for the year after the Sarbanes-Oxley Act is given as 10.65257

After the enactment of the Sarbanes-Oxley Act, was the average bank’s ROE lower than it was before the act? If so, why do you think that was the case?

After the enactment of the Sarbanes-Oxley Act, average bank’s ROE was not lower than it was before the act. It is observed that the average return on equity is increased after the enactment of the Sarbanes-Oxley Act.

What is the null hypothesis for this hypothesis test?

Null hypothesis: H0: There is no any statistically significant difference in the average return on equity after the enactment of the Sarbanes-Oxley Act and before the enactment of the Sarbanes-Oxley Act.

What is the alternative hypothesis for this hypothesis test?

Alternative hypothesis: Ha: The average return on equity before the enactment of the Sarbanes-Oxley Act is lower than the average return on equity after the enactment of the Sarbanes-Oxley Act.

Choose at least three different significant levels to conduct the hypothesis test.

Consider three significant levels such as 1%, 2% and 5%.

Alpha = = 0.01, 0.02, 0.05

Here, we have to use paired t test for checking the significant difference between two population means. The test statistic formula is given as below:

t = dbar/[SD/sqrt(n)]

for the given data, we are given

dbar = 4.822025

SD = 7.926472

n = 20

so, degrees of freedom = df = 20 – 1 = 19

t = 4.822025/(7.926472/sqrt(20))

t = 2.720599

P-value = 0.0068

For = 0.01, 0.02, 0.05, P-value is less.

P-value < , so we reject the null hypothesis that There is no any statistically significant difference in the average return on equity after the enactment of the Sarbanes-Oxley Act and before the enactment of the Sarbanes-Oxley Act.

There is sufficient evidence to conclude that average return on equity before the enactment of the Sarbanes-Oxley Act is lower than the average return on equity after the enactment of the Sarbanes-Oxley Act.

It is possible that a Type I error occurred with the hypothesis test because there is a chance of equal average return on equity after and before the act.

It is possible that a Type I error occurred with the hypothesis test because there is a chance of do not rejecting null hypothesis even though average returns on equity before and after act are same.

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