# Null Hypothesis  ## What is the Null Hypothesis Formula?

Null hypothesis presumes that the sampled data and the population data have no difference or in simple words, it presumes that the claim made by the person on the data or population is the absolute truth and is always right. So, even if a sample is taken from the population, the result received from the study of the sample will come the same as the assumption.

It is denoted by H0 (pronounced as ‘H not’).

### How does it work?

In the initial claim of the null hypothesis, it is assumed that the assumption is true. For example, assume that there is a claim which states it takes 30 days to form any habit. Therefore here, it will be assumed that it is true 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 form of a mathematical model that is used to accept or reject the hypothesis within a range of confidence levels.

There are 4 steps that are to be followed in this model.

1. The first step is to state the 2 hypotheses, namely the null hypothesis and alternative hypothesis so that only one of them can be right.
2. The second step involves a strategy which states various methods through which the data will be analyzed.
3. The third step consists of actually analyzing the required set of data to make conclusions.
4. The last and fourth step is to analyze the results and make a decision to accept or reject the hypothesis.

### Null Hypothesis Formula

Null Hypothesis Formula (H0): Parameter = Value”

Where,

• The parameter is the assumption or statement made by the concerned party or person.

A through the level of significance of the observed data for summarizing the theoretical data. For calculation of Deviation from the Claimed data, we can use the formula;

Deviation Rate = Difference between observed data & theoretical data/theoretical data.

The measurement of deviation is a mere tool to study the level of significance of the states claimed in the Null Hypothesis Testing.

For eg:
Source: Null Hypothesis (wallstreetmojo.com)

### Examples of Null Hypothesis Testing

Concept 1: Null Hypothesis should have a sign of equality, or in other words, this Hypothesis means the assumption of no difference.

#### Example #1

A research team comes to the conclusion that if children under age 12 consume a product named ‘ABC’, then the chances of their height growth increased by 10%. But by evaluating the sample growth rate checked by choosing some children who are consuming the product ‘ABC’ comes to be 9.8%. Explain the null hypothesis in the provided case.

Solution: In this case, if a null hypothesis assumption is taken, then the result selected by the researcher will be as per the criteria;

H0: Parameter = value

Where the parameter selected by the researcher is that that on the consumption of product ‘ABC’ by the children under age 12, there is a chance of an increase in growth rate by 10%.

The value of the parameter is @ 10%

Thus on presuming the null hypothesis, the researcher will take the value of parameter @ 10% as the assumption has been taken.

Concept 2: Level of significance, as mentioned in the definition, is the measuring of reliability of the actual data in comparison to the data assumed or claimed in the statement made.

The level of significance can be tested through the valuation of deviation in the observed data and the theoretical data.

#### Example #2

In a study by the authority of an industry, they claim that on average production of 100 goods, the chances of a faulty good’s production come out to be 1.5 %. But during the study of a sample taken, the chances of fault good’s production comes out to be nearly 1.55%. Comment on the following situation.

Solution

In the case of the Null Hypothesis Testing, the fact assumed to be the correct world be the claim made by the authority that the chances of fault good’s production are 1.5 % for the production of every 100 goods.

In this case, the level of significance can be measured through deviation.

Calculation of Deviation Rate can be done as follows,

• =(1.55%-1.50%)*100/1.50%

Deviation Rate will be –

• Deviation Rate = 3.33%
##### Explanation

In this example, the deviation from the assumed parameter comes out to be 3.33 %, which is in 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 in the case, such deviation would have exceeded 5% or more (differs from condition to condition), the hypothesis needed to be rejected because the assumption made would have no ground to be justified.

Concept 3: There are many different ways to verify the statement presumed in case of the ‘null hypothesis,’ one of the methods is to compare the Mean of the sample taken with the Mean of the population. Where the term ‘Mean’ could be defined as the average of the value of the parameter taken to the number of data selected.

#### Example #3

An organization of experts after their study claimed that the average working time of an employee working in the manufacturing industry comes about to be 9.50 hours per day for proper completion of work. But a manufacturing company named XYZ Inc. claimed that the average hours worked by their employees is less than 9.50 hours per day. For studying the claim, a sample of 10 employees was taken, and their daily working hours are recorded below. The mean of the sample data selected is 9.34 hours per day—comment about the claim by XYZ Inc.

Solution

Let’s take the Null Hypothesis formula for analyzing the situation.

H0: Parameter = value i.e.,

Where,

• Parameter taken by the experts is ‘average working hour of the employee working in a manufacturing company.’

The value taken by the experts is 9.50 hours per day.

• Mean (average) of the working hours of population = 9.50 hours per day
• Mean (average) working hours of the sample = 9.34 hours per day

Calculation of Deviation Rate can be done as follows,

• =(9.50-9.34)*100%/9.50

Deviation Rate will be –

• Deviation Rate = 1.68%
##### Explanation

In the above example, the statement made by the experts claimed that the average working hour of an employee working in the manufacturing industry is 9.50 hours per day. Whereas in the study of the sample taken, the average of the working hours comes out to be 9.34 hours per day. In the case of the ‘null hypothesis,’ the statement is taken, or the claim made by the experts is taken as a parameter, and the value of the parameter is also believed to be the 9.50 hour per day, as claimed by the statement. But we can see that after the study of the sample, the average hour comes out to be less than the claimed hour. In case of such presumption, such a hypothesis is called as ‘Alternate hypothesis.’

• It is Provides a Logical Framework for Testing Statistical Significance: It helps to test certain hypotheses with the help of statistics.
• Technique is Tried and Tested: The method has been tested in recent times, and it helps to prove certain assumptions.
• Alternate Hypothesis, which is the Opposite of the Null Hypothesis, can be Vague:  So, for example, if this says mutual fund returns are 8%, then the alternate hypothesis will be the mutual fund returns are not equal to 8%. In a two-tailed test, the returns can be proved to be greater than or less than equal to 8%.
• It Reflects the same Underlying Statistical Reasoning as Confidence Intervals:  is used for confidence interval testing.

• It is Commonly Misunderstood and Misinterpreted: Sometimes, it is difficult to state the null hypothesis and an appropriate alternative hypothesis. This is the first step, and if it fails, then the entire experiment of analyzing the hypothesis will go wrong.
• P-Value Test is Uninformative Compared to Confidence Interval: The confidence interval of 5% may not be significant most of the time.
• This is Nearly always False: Nearly always, we try to prove that there is statistical significance to reject the null hypothesis. In very few cases, this hypothesis is accepted.

### Relevance and Use

The Null Hypothesis is mainly used for verifying the relevance of Statistical data taken as a sample comparing to the characteristics of the whole population from which such sample was taken. In simple words, if any assumption has been made for the population through the sample data selected, then the null hypothesis is used for verifying such assumptions and evaluating the significance of the sample.

The null hypothesis is also generally used for verifying the difference between the alternative procedures. For example, let’s say there are two ways to treat disease, and it is claimed that one has more effects than the other. But the null hypothesis presumes that the effects of both the treatments are the same, and then the study is being done for finding the significance of such assumption and the variance of such.

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