Null Hypothesis

Updated on March 14, 2024
Article byWallstreetmojo Team
Edited byAshish Kumar Srivastav
Reviewed byDheeraj Vaidya, CFA, FRM

What is Null Hypothesis?

The null-hypothesis is considered an accepted truth. It assumes that the research is false, that the observations are caused by random factors. Researchers must prove the null-hypothesis wrong to prove their alternate hypothesis.

The null-hypothesis presumes that the sampled data and the population data have no difference. It is the opposite of the alternate hypothesis, which says that the sample or claimed data differs from the actual population. The null-hypothesis is denoted by H0 (pronounced as ‘H naught’).

Key Takeaways

  • During, Null Hypothesis Significance Testing (NHST), if the level of significance is within the acceptable limit or confidence interval, H0 is accepted; otherwise, it is rejected.
  • Hypothesis testing is a form of a mathematical model that is used to accept or reject a hypothesis within a range of confidence levels.
  • Null hypothesis is an assumption that is accepted valid unless proven otherwise. It is used for prove or dissprove research statements along with statistical data.

Null Hypothesis Explained

A null-hypothesis can be defined as an accepted fact that may or may not be true. In the initial claim of the null-hypothesis, it is believed that the assumption is valid. The null hypothesis is mainly used for verifying the relevance of Statistical data taken as a sample. This sample is then compared to the characteristics of the whole population from which the sample was taken. Researchers can prove or disprove a statement or assumption by conducting Hypothesis Testing (NHST).

For example, assume that a claim states it takes 30 days to form a habit. Therefore, it will be considered that it is valid until there is some statistical significance to prove that our assumption is wrong, and it does not take 30 days to form a habit. Hypothesis testing is a mathematical model used to accept or reject the hypothesis within the prescribed range of confidence level. It is also used for verifying the difference between alternative procedures.

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The null hypothesis serves as a base for prominent scientific research. For example, scientists believe that “there is life on Mars,” The statement could be accepted or rejected based on statistical analysis.

Null theory formula

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Null Hypothesis Formula

Based on the null hypothesis, we need to prove that:

H-naught theory formula
H-naught Hypothesis explanation

A hypothesis is tested for significance levels level in the observed data. This is done for summarizing theoretical data.

For calculation of deviation from the claimed data, we can use the formula:

For calculation of deviation (Null Theory)

How to find the null-hypothesis?

Some of the basic steps to determine H0 are as follows:

  1. The first step is to assume that the given statement is true.
  2. Next, find the level of significance or the deviation rate. For this first find the difference between claimed data and the actual data and then divide it by claimed data. The result is multiplied by 100.
  3. If the result falls within the confidence interval, then the null hypothesis is accepted; however, the hypothesis is rejected if it is outside the confidence interval. Here, we see that the claimed or assumed value has to be equal to or nearly equal to the actual data for the null hypothesis to be true.

Null Hypothesis Examples

Now let us apply the null hypothesis to a few examples.

In an industrial study, it was claimed that on average production of 100 goods, the chance of encountering a faulty product was only 1.5 %. But during the study of a sample taken, it was found that the chances of encountering a faulty product were actually 1.55%. Comment on this condition.


In the case of the Null-Hypothesis Testing, the original claim is assumed to be correct. Here, it is assumed only 1.5 %  of 100 goods were faulty products.

H-naught Theory Examples 1

In this case, deviation helps ascertain the level of significance.

Calculation of Deviation Rate can be done as follows:

H-naught Hypothesis Examples 1-1

= (1.55%-1.50%) * 100/1.50%

Therefore, the Deviation Rate will be:

Null Hypothesis Examples 1-2

Deviation Rate = 3.33%


In this example, the standard deviation from the assumed parameter is 3.33 %, which falls within the acceptable range, i.e., 1% to 5%. Thus, the null hypothesis can be accepted even when the actual valuation differs from the assumption. But if such deviation exceeds 5%, the hypothesis will be rejected. Beyond that percentage, the assumption made will have no justification.

There are many ways to verify a presumed statement. For example, with null assumptions, the mean of the sample is compared to the population mean. Here, the term ‘mean’ could be defined as the average value of the parameter and the number of variables.


While we conduct various statistical tests like P-value, the results can be analyzed by determining the null-hypothesis and alternative hypothesis. Some of the reasons for its importance are discussed below:

  • Logic Behind Statistical Significance Testing: Statistics is used to test if the assumptions occur by chance or for particular reasons. It helps in ruling out random factors causing an observation.
  • Prove or Disprove Relational Statement: Null-hypothesis proves that there is no relation between two variables; thus, it is used for relational inference.
  • Facilitates Alternate Hypothesis Testing: The alternate hypothesis is just one side of the coin. The null-hypothesis is essential for finding and validating its result.
  • Confidence Interval: It reflects the same underlying statistical reasoning as P-value in excel.
  • Applicable in Different Fields of Study: Whether research, science, psychology, statistics, or investment, everything requires hypothesis testing


The null-hypothesis is based on analysis; therefore, interpretation is critical. Unfortunately, it can be easily misinterpreted and manipulated. In most cases, the significance testing is usually conducted to get rejected; thus, the results often come out false.

Another significant issue is selecting an appropriate sample size for finding the probability or mean. A small sample size fails to provide accurate results. Similarly, a huge sample complicates the calculation.

Null Hypothesis vs. Alternate Hypothesis

Null-hypothesis refers to a statistical approach where the sample value deems to be the same as the population data. In this condition, their statistical significance lies somewhere within the confidence level. In contrast, for an alternate hypothesis, the sample value differs from the population data. In such a case, the statistical significance of these two values does not fall within the confidence level.

The null-hypothesis signifies the possibility of observations being caused by chance or random factors. In contrast, the alternate hypothesis highlights that the observations were caused by specific reasons.

Frequently Asked Questions (FAQs)

What is a null-hypothesis example?

The null-hypothesis validates sample data being equivalent to the population data. This means that these two values have no statistical significance. One example is that a doctor states that a human being takes five days on average to recover from viral fever. Based on 50 patients, the average recovery rate is 4.97 days, which is approximately equal to 5 days. Thus, the null assumption is valid. The sample was taken from various states.

When to accept the null-hypothesis?

The null-hypothesis is accepted when the sample value is equal to or almost identical to the population data. In such a case, the statistical significance falls within the given cut-off confidence interval. Conversely, if the sample data is not equal to the population data or if the statistical significance level is below the confidence interval, the hypothesis is rejected.

Why is hypothesis testing important?

Hypothesis testing is essential for the validation of sample data concerning population data. Moreover, it helps draw a meaningful conclusion in medical science, research, psychology, and statistics.

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