# Tutor profile: Abdelhak K.

## Questions

### Subject: Finance

Evaluate the following statement: "Investing in the stock market is pure gambling"

In order to evaluate whether this statement is correct or not, we should first understand the similarities and differences between pure gambling and investing in the stock market. in the outset, they both deal with uncertainty; any outcome cannot be known in advance nor can it be determined with certainty, and it can only be estimated or guessed. In gambling, the probability that an outcome might occur -success or failure- is usually referred to as a chance, and the principles of statistics are applied to determine its likelihood with utmost precision. In investment, however, principles of finance are applied to determine the probability of success or failure. Success is usually referred to as return on investment (ROI), while failure is referred to as risk. The biggest difference between gambling and investment is that in the former, the outcome is uncertain but it's chance is certain and can be known in advance. Consider flipping a coin, we cannot know whether it's head or tail until we flip the coin, but we already know that the likelihood of getting head on the first attempt is 50%. An investor can never know for certain the outcome nor its likelihood in advance. If he intends to buy 100 shares in any company in the stock market, he does not know for certain whether the prices of the shares would increase nor does he know the probability of it happening, as opposed to flipping a coin. This is the very reason why investors rely heavily on mathematics, statistics, and other social sciences to create models they use to predict the ROI and Risks. Investors, therefore, speculate, and they based their speculations on models, historical data, macro and micro economical factors, and their experience to invest. It is this rigorous process that makes investment an educated guess rather than pure lucky guess. Therefore, if an investor buys shares in the stock market based on none but his or her guts without any rational behind, then he is gambling. But, if he or she uses principles of finance and investment to evaluate the ROI and risks, uses a rigorous process, understands the economical factors and historical data prior to purchasing or selling stocks, then he or she is investing.

### Subject: Statistics

In hypothesis testing, when should one use z-test and t-test generally?

Z-test and T-test are two important data validation tests used in inferential statistics; researchers use data gathered from a random sample to draw or infer conclusions about the entire population. In other words, what they find true about a sample is assumed to be true about the population. Therefore, the answer to the question depends of 2 factors: how well we know the population, and how large is our sample size. If we have good knowledge about the population parameters (the mean and standard deviation are known) and we have a fairly large sample size (30 or more), then the Z-test is preferable, simply because it uses population parameters. Consider this hypothetical example. A team of researchers developed a new drug that they believe to improve life expectancy in cancer patients. The researchers want to test this new drug within a population of mice. From historical data, they know that the average life expectancy of mice with cancer is about 2 years, with a standard deviation of 1.2 year. The team then injects the drug to 100 sick mice (sample size = 100) and observes their life expectancy. In this case, the Null hypothesis would be that sample mean is same as the population mean, or Null: sample mean equals 2. And, the Alternative hypothesis would be Sample mean is not the same as the population mean, or Alternative: sample mean is different from 2. Since, in this case, parameters about the population are known, and the sample size is large, the researchers can use z-test. If the test statistic is lower than the critical value, then we accept the Null, and there are enough evidence for the researchers to conclude that the drug has little or no effect. If the Null is rejected, then there is enough evidence to conclude that the drug is effective. On the other hand, if population parameters are unknown and/or the sample size if relatively small (less than 30), then a t-test is preferable. In this case, it is difficult to compare a sample to the population. We can take two random samples and analyze how significant the difference between the two using t-test. In an essence, t-test lets you know if the differences in the two samples (their means) could have happened by chance. Consider the previous example with one difference; the team of researchers does not know the average life expectancy of ill mice. In order to know whether the drug is effective against cancer, the team would take to different samples of sick mice: one group will not be injected with the drug, which serves as a control group, and the second group is being injected with the drug and would serve as the test group. The former is a proxy of the population and the researchers assume that data collected from this group would reflect the entire population. Data collected from both groups show that the average life expectancy in the control group is 2 years, and within the test group the average is 3 years. The results may indicate that the drug is effective. However, there is a probability that this difference in the average between the two groups is by chance. T-test would allow the researchers to measure how significant the difference between the average life expectancy in the two samples. If the difference is significantly large, then the drug is effective. The p-value is the probability that the results from the test group is due to luck. The lower the p-value is, the less likely the result are due the chance. If the p-value is larger than the significant level (alpha), the we accept the Null, and we can safely conclude that the results from the drug are due the chance, and therefore, the drug has little or no effect. If the p-value is larger than alpha, then we reject the Null, and we can safely assume that the drug is effective. To sum up, both the Z-test and T-test help us infer information about the population using samples. If we have good knowledge about the population and we have a fairly large sample size, then we use Z-test. Otherwise, T-test is better.

### Subject: Accounting

Is Capital different from Equity? If yes, how is it different?

The short answer is yes; Capital is different from Equity. In fact, Capital is a part of Equity. At its most basic form, accounting is the way by which a company tracks records of every transactions it has made during the course of its business activity to help management answer the following question: "how did the company pay for all the assets it owns?". The answer to this question is depicted in the Balance Sheet (BS), where one side encompasses all the assets the company owns, and the other side of the BS encompasses the sources of the money the company used to pay off those assets it owns. Typically, a company's asset is either paid by a debt from an external party, by owners, or a combination of both. Liability is the share of the asset owned by the external party, and Equity is the share of the asset paid by the owner. At the moment of it's inception, the company has to borrow money from its owner in order to buy assets it uses during the course of its business activity. This money is called Capital. By using its assets, the company may generate profits, and any profit it makes goes to the owner. In the course of many fiscal years, profits would accumulate. These accumulated profits are called Reserves. The company may also use its own reserves to finance the purchase of new assets. Because these new assets are financed by reserves which are basically the owner's money, they are also part of Equity. Hence, Equity = Capital + Reserves. Therefore, Capital is different from Equity. To sum up, accounting helps track which portion of a company's assets is financed by liabilities, which is financed by owner's capital, and which is financed by reserves (accumulated profits). Since both reserves and capital belong to the owner, they form the owner's Equity. This is depicted in the basic Accounting Equation Formula: Assets = Liability + (Capital + Reserves) or Assets = Liabilities + Equity.

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