# Null Hypothesis ## What is a null hypothesis?

A null hypothesis is a type of hypothesis used in statistics which proposes that no statistical significance exists in a given set of observations. The null hypothesis attempts to show that there is no variation between the variables or that a single variable is not different from its mean. It is presumed to be true until statistical evidence invalidates it for another hypothesis.

For example, if the hypothesis test is configured so that the alternative hypothesis indicates that the population parameter is not equal to the claimed value. Therefore, the cooking time for the average population is not equal to 12 minutes; it could rather be lower or higher than the value indicated. If the null hypothesis is accepted or if the statistical test indicates that the population average is 12 minutes, the alternative hypothesis is rejected. And vice versa.

### Key points to remember

• A null hypothesis is a type of conjecture used in statistics which suggests that no statistical significance exists in a given set of observations.
• The null hypothesis is posed in opposition to an alternative hypothesis and attempts to show that there is no variation between the variables, or that a single variable is not different from its mean.
• The hypothesis test allows a mathematical model to validate or reject a null hypothesis within a certain level of confidence.

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## How a null hypothesis works

The null hypothesis, also known as guesswork, assumes that any type of difference or meaning you see in a data set is due to chance. The opposite of the null hypothesis is known as the alternative hypothesis.

The null hypothesis is the initial statistical assertion that the average of the population is equivalent to the alleged. For example, suppose the average cooking time for a specific brand of pasta is 12 minutes. Consequently, the null hypothesis would be formulated as follows: “The average of the population is equal to 12 minutes”. Conversely, the alternative hypothesis is the hypothesis which is accepted if the null hypothesis is rejected.

The hypothesis test allows a mathematical model to validate or reject a null hypothesis within a certain level of confidence. Statistical assumptions are tested using a four-step process. The first step is for the analyst to state the two hypotheses so that only one can be right. The next step is to formulate an analysis plan, which describes how the data will be evaluated. The third step is to execute the plan and physically analyze the sample data. The fourth and final step is to analyze the results and accept or reject the null hypothesis.

### Important

Analysts look to to reject the null hypothesis to exclude one or more variables explaining the phenomena of interest.

## Example of null hypothesis

Here is a simple example: A school principal reports that students in her school get an average of 7 out of 10 on exams. To test this “hypothesis”, we record scores of about 30 students (sample) from the entire student population of the school (say 300) and calculate the average of this sample. We can then compare the average of the sample (calculated) with the average of the population (declared) and try to confirm the hypothesis.

Let’s take another example: the annual return of a particular mutual fund is 8%. Suppose the mutual fund has been in existence for 20 years. We take a random sample of annual fund returns for, say, five years (sample) and calculate its average. We then compare the mean (calculated) of the sample with the mean (claimed) of the population to verify the hypothesis.

Usually, the declared value (or claim statistics) is indicated as an assumption and presumed to be true. For the above examples, the assumption will be:

• Example A: School students get an average of 7 out of 10 on exams.
• Example B: The annual yield of the UCI is 8% per year.

This declared description constitutes the “Null hypothesis (H0)” and is assumed to be true – the way an accused in a jury trial is presumed innocent until proven guilty by the evidence presented in court. Similarly, the hypothesis test begins by stating and assuming a “null hypothesis”, then the process determines whether the hypothesis is likely to be true or false.

The important point to note is that we are testing the null hypothesis because there is an element of doubt about its validity. Whatever information is contrary to the stated null hypothesis, it is Alternative hypothesis (H1). For the above examples, the alternative hypothesis would be:

• Students get an average which is do not equal to 7.
• The annual yield of the mutual fund is do not equal to 8% per year.

In other words, the alternative hypothesis is a direct contradiction of the null hypothesis.

## Hypothesis test for investments

As an example related to the financial markets, let’s assume that Alice sees that her investment strategy produces higher average returns than just buying and holding a stock. The null hypothesis claims that there is no difference between the two average returns, and Alice must believe it until she proves otherwise. To refute the null hypothesis, one would have to show statistical significance, which can be found using a variety of tests. Therefore, the alternative hypothesis would indicate that the investment strategy has a higher average return than a traditional buy and hold strategy.

The p-value is used to determine the statistical significance of the results. A p-value less than or equal to 0.05 is generally used to indicate whether there is strong evidence against the null hypothesis. If Alice performs one of these tests, such as a test using the normal model, and proves that the difference between her yields and the purchase and conservation yields is significant, or that the value of p is less than or equal at 0.05, it can then refute the null hypothesis and accept the alternative hypothesis.