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# Hypothesis Testing: Banking Industry

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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. Please obtain the required data from the attached Excel documents.

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.

•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?

#### Solution Preview

I sort the banks alphabetically, and I am picking the first 20 banks.

These are their ROEs in 2001 and 2003

13.674364 19.30522888
15.27789599 24.11508282
14.74781183 3.877061028
13.90273781 19.29439865
13.60481354 10.25927786
6.282033837 7.461413831
4.154114476 6.670533643
5.73816156 6.092211717
-0.176437813 3.068478605
13.19110078 22.02703256
13.58641368 13.52275765
9.903245854 9.090319577
-31.03349906 18.37416481
17.8522384 7.238626836
2.452776147 36.75262181
54.1323618 5.380385857
8.336905669 15.04008449
13.01442333 17.56965198
16.59451659 16.90804985
19.04079632 7.417149019

In a separate excel sheet, we copy these 40 numbers. The average of ...

#### Solution Summary

The return on equity for a sample of 20 banks before and after the Sarbanes-Oxley Act was enacted is calculated. The null and alternative hypothesis for this hypothesis test is provided. The expert chooses at least three different significant levels to conduct hypothesis tests.

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Please solve the exercise below in Excel and show your work (and formulas)

1. At &#945; =..05 and .10, test the hypothesis that the proportion of Consumer (CON) industry companies winter quarter profit growth is more than 2% greater than the proportion of Banking (BKG) companies winter quarter profit growth, given that p CON = 0.20, p BKG = 0.14, nCON = 350, nBKG = 400.

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