What is the Null Hypothesis?

A null hypothesis refers to a kind of statistical hypothesis that signifies the absence of statistical significance for a group of specific observations. It showcases that there is not any variation involved between variables. Or, it can state that one variable is similar to its mean. It is considered to be accurate until an alternative hypothesis proves it wrong. For instance, in case, the hypothesis test is conducted in such a manner that the alternative hypothesis showcases a difference between the population parameter and the claimed amount. Hence, the population means cook time is not equivalent to 12 minutes. Instead, it tends to be different, either more or less than the given value. In case, the null hypothesis is true, or the hypothesis test says that the population mean tends to be 12 minutes, then it will automatically lead to the elimination of the alternative hypothesis, and vice-versa. 

Key Points to Remember

1. A null hypothesis refers to a statistical approach that involves no statistical relation in the group of said observations.
2. The null hypothesis is created against an alternative hypothesis with an objective to display no existing variations between variables. In other words, it says that there is no difference between the mean and a variable.
3. Hypothesis testing, by using a certain confidence level, lets a statistical model to either accept or neglect a null hypothesis.

How is the Null Hypothesis Used? 

Null hypothesis is also referred to as the conjecture. It is based on the belief that odds are responsible for creating any sort of difference or variations in a given set of variables. In contrast to the null hypothesis, there exists another hypothesis known as alternative hypothesis. The null hypothesis refers to the first claim that the value of the population mean tends to be equal to the claim value. For instance, a particular pasta brand takes 12 minutes on an average to cook well. Hence, the null hypothesis for this assumption would be: The population mean is equivalent to 12 minutes. In case, there is a rejection of the null hypothesis, the alternative hypothesis would be accepted in return. A statistical model can accept or reject a null hypothesis falling in a specific confidence interval by using hypothesis testing. This test involves four steps which are:

1. First of all, the statistician should state null and alternate hypothesis, out of which only one would be accurate.
2. The second step is to create an analysis strategy in order to evaluate the information.
3. The third step is to implement the plan or strategy created in the second step, and do sample data analysis.
4. The last step is to compare the results, and find out which hypothesis, null or alternate, needs to be accepted.

Statisticians are more keen to reject or eliminate the null hypothesis for eliminating at least one variable.

Examples of setting up a null hypothesis

Lets take this example. As per a college principal, the students secured 7/10 marks on an average in tests. For this hypothesis test, we took a sample size of 30 students from the total population of 300 students in the school. We ascertained the sample mean, and compared the calculated mean with the population mean, and then take decision about the hypothesis. In another example, a specific mutual fund offers an annual rate of return of 8%. Lets say that this mutual fund has been operating for a period of 20 years. We took a random sample of mutual funds returns received per year for 5 years, and then determine its average or mean. The next step is to strike a comparison with the sample mean calculated for 5 years, and the population mean for coming to a conclusion. Generally, the reported number is referred to as the hypothesis, and assumed to be right. For the aforementioned instances, hypothesis will be:

1. For the first example, students secure a score of 7 out of 10 in school exams.
2. For the second example, the yearly rate of return for the mutual fund is 8%.

The above two statements which form the null hypothesis are assumed to be correct. It is similar to the court proceedings where an accused is presumed to be non-guilty until the other party presents evidence against him, and proves him guilty. Similarly, the first stage of hypothesis testing is to create a null hypothesis, and determine if this presumption is right or wrong. The null hypothesis is tested for ensuring its validity and reliability. Any data that is in contrast to the null hypothesis is stored in alternate hypothesis. Hence, the alternate hypothesis for the above two instances would be:

1. The average score of school students is not equal to 7.
2. The yearly rate of return on mutual funds is not equal to 8% p.a.

Therefore, it is right to say that the alternate hypothesis is exactly the opposite of the null hypothesis.

Hypothesis Testing for Investments

Considering an instance from financial markets, lets suppose that Mr. A believes that his investment strategy would offer more returns on an average as compared to merely purchasing and holding a stock. As per the null hypothesis, two average returns dont show any difference or variations. Mr. A needs to agree to this hypothesis until he proves it wrong. For doing so, he needs to consider using different tests. Hence, the alternate hypothesis would show that the investment strategy offers more average rate of return as compared to a basic buy-and-hold investment strategy. Analysts use the p-value for knowing the mathematical importance of the outcomes. If the p-value is either equal to or lower than 0.5, it shows a big evidence that is not in favor of the null hypothesis. In case, Mr. A uses any of the tests, and finds out that there is a significant level of difference in his returns and the buy-and-hold returns, then he can agree to the alternate hypothesis and reject the null hypothesis.