Hypothesis Testing
In the banking industry, the return on equity ratio or percentage is used to evaluate the financial performance of a bank. Such information is extremely valuable to investors.
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?
Submit your answers in an eight- to ten-page Word document.
Assignment explanation help
1. Please see attached excel template- You will be using this template to complete the assignment. The cells highlighted in Yellow are input cells and the formulas are already plugged in for your convenience.
2. Now its time to understand what the term Return on Equity (ROE) means.
Return on equity measures a corporation's profitability by revealing how much profit a company generates with the money shareholders have invested. ROE is expressed
as a percentage and calculated as: Return on Equity = Net Income/Shareholder's
Equity. The ROE is useful for comparing the profitability of a company to that of other
firms in the same industry. Please look at this video for a primer on
ROE: https://www.youtube.com/watch?v=p6c37YxFnmg
3. Pick 20 publicly traded (traded on stock exchange) banks which existed back then and research over the internet the annual ROE for those 20 banks in 2001 and again for the same banks in 2003 (after implementation of SOX act) and enter into the excel file. Typically you can go online to a website like Wikinvest and type the name of the bank and get the historical ROE right from 1990s to date. But you only need annual ROE for 2001 and 2003. For example, I searched for Bank of America ROE and I used the Wikinvest link and found the
data: https://www.wikinvest.com/stock/Bank_of_America_(BAC)/Data/ROE/2001
4. Sarbanes Oxley Act (SOX) was implemented in 2002. The objective of the assignment is to examine the ROE before (2001) and after (2003) implementation of SOX. For information on SOX and to get a quick primer please
visit: https://www.investopedia.com/terms/s/sarbanesoxleyact.asp
There is also a good article on SOX and it can be found
at: https://www.nysscpa.org/cpajournal/2008/808/perspectives/p13.htm
5. Since we are examining the ROE for the same banks in 2001 and 2003, we will
use the "t tests for paired samples". Please refer to Chapter 10, Section 10.4
Comparing Two Means: Paired Samples for reference. The excel template
attached is already setup for t tests for paired samples.
6. For the Assignment, you will also have to state the Null and Alternate Hypothesis.
The Null Hypothesis denoted by H0 should state that there is NO difference in ROE
between 2001 and 2003. The Alternate will indicate that the ROE will be different,
which is denoted by HA
7. Once you plug the values of ROE (2001 and 2003) in Excel and calculate the t (test statistic) values as well as the t(critical) values from the "t table" (can be found in Appendix D of text book) for 3 different significance values. If t (test statistic) > t (critical) from table, then the result is significant, which means for that particular significance level, the result is significant. In general, when the result is significant, you reject the Null Hypothesis. Remember you can pick any significance levels, and you might get different answers on accepting/rejecting the hypothesis.
8. The concluding part of the assignment asks for whether there is a YPE I (α) or II (β) error. Please carefully read Chapter 9, Section 9.1, Types of Error (Page 345) for information on this topic.In general, α is also the significance level which you picked on the t table. α and β are in a mutually inverse relationship, such that as you decrease α, the chances of β goingup are increased and vice versa.
Attachment:- excel_template.xlsx