Alternative Hypothesis

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Alternative hypothesis defines there is a statistically important relationship between two variables. Whereas null hypothesis states there is no statistical relationship between the two variables. In statistics, we usually come across various kinds of hypotheses. A statistical hypothesis is supposed to be a working statement which is assumed to be logical with given data. It should be noticed that a hypothesis is neither considered true nor false.

Null Hypothesis
T-Test Formula
P-value
Hypothesis Testing Formula

Definition

The alternative hypothesis is a statement used in statistical inference experiment. It is contradictory to the null hypothesis and denoted by H_a or H₁. We can also say that it is simply an alternative to the null. In hypothesis testing, an alternative theory is a statement which a researcher is testing. This statement is true from the researcher’s point of view and ultimately proves to reject the null to replace it with an alternative assumption. In this hypothesis, the difference between two or more variables is predicted by the researchers, such that the pattern of data observed in the test is not due to chance.

Example

To check the water quality of a river for one year, the researchers are doing the observation. As per the null hypothesis, there is no change in water quality in the first half of the year as compared to the second half. But in the alternative hypothesis, the quality of water is poor in the second half when observed.

Difference Between Null and Alternative Hypothesis

Null Hypothesis	Alternative Hypothesis
It denotes there is no relationship between two measured phenomena.	It’s a hypothesis that a random cause may influence the observed data or sample.
It is represented by H₀	It is represented by H_a or H₁
Example: Rohan will win at least Rs.100000 in lucky draw.	Example: Rohan will win less than Rs.100000 in lucky draw.

Types

Basically, there are three types of the alternative hypothesis, they are;

Left-Tailed: Here, it is expected that the sample proportion (π) is less than a specified value which is denoted by π₀, such that;

H₁ : π < π₀

Right-Tailed: It represents that the sample proportion (π) is greater than some value, denoted by π₀.

H₁ : π > π₀

Two-Tailed: According to this hypothesis, the sample proportion (denoted by π) is not equal to a specific value which is represented by π₀.

H₁ : π ≠ π₀

Note: The null hypothesis for all the three alternative hypotheses, would be H₁ : π = π₀.