What type of hypothesis states that there is difference between a parameter and a specific value or that there is no difference between two parameters?

The alternative hypothesis is one of two mutually exclusive hypotheses in a hypothesis test. The alternative hypothesis states that a population parameter does not equal a specified value. Typically, this value is the null hypothesis value associated with no effect, such as zero. If your sample contains sufficient evidence, you can reject the null hypothesis and favor the alternative hypothesis. The alternative hypothesis is often denoted as H1 or HA.

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How the Null Hypothesis Works
Null Hypothesis Example
What is an Alternative Hypothesis?
Purpose of Hypothesis Testing
Additional Resources

If you are performing a two-tailed hypothesis test, the alternative hypothesis states that the population parameter does not equal the null hypothesis value. For example, when the alternative hypothesis is HA: μ ≠ 0, the test can detect differences both greater than and less than the null value.

A one-tailed alternative hypothesis can test for a difference only in one direction. For example, HA: μ > 0 can only test for differences that are greater than zero.

How the Null Hypothesis Works

A null hypothesis is a theory based on insufficient evidence that requires further testing to prove whether the observed data is true or false. For example, a null hypothesis statement can be “the rate of plant growth is not affected by sunlight.” It can be tested by measuring the growth of plants in the presence of sunlight and comparing this with the growth of plants in the absence of sunlight.

Rejecting the null hypothesis sets the stage for further experimentation to see a relationship between the two variables exists. Rejecting a null hypothesis does not necessarily mean that the experiment did not produce the required results, but it sets the stage for further experimentation.

To differentiate the null hypothesis from other forms of hypothesis, a null hypothesis is written as H0, while the alternate hypothesis is written as HA or H1. A significance test is used to establish confidence in a null hypothesis and determine whether the observed data is not due to chance or manipulation of data.

Researchers test the hypothesis by examining a random sample of the plants being grown with or without sunlight. If the outcome demonstrates a statistically significant change in the observed change, the null hypothesis is rejected.

Null Hypothesis Example

The annual return of ABC Limited bonds is assumed to be 7.5%. To test if the scenario is true or false, we take the null hypothesis to be “the mean annual return for ABC limited bond is not 7.5%.” To test the hypothesis, we first accept the null hypothesis.

Any information that is against the stated null hypothesis is taken to be the alternative hypothesis for the purpose of testing the hypotheses. In such a case, the alternative hypothesis is “the mean annual return of ABC Limited is 7.5%.”

We take samples of the annual returns of the bond for the last five years to calculate the sample mean for the previous five years. The result is then compared to the assumed annual return average of 7.5% to test the null hypothesis.

The average annual returns for the five-year period are 7.5%; the null hypothesis is rejected. Consequently, the alternative hypothesis is accepted.

What is an Alternative Hypothesis?

An alternative hypothesis is the inverse of a null hypothesis. An alternative hypothesis and a null hypothesis are mutually exclusive, which means that only one of the two hypotheses can be true.

A statistical significance exists between the two variables. If samples used to test the null hypothesis return false, it means that the alternate hypothesis is true, and there is statistical significance between the two variables.

Purpose of Hypothesis Testing

Hypothesis testing is a statistical process of testing an assumption regarding a phenomenon or population parameter. It is a critical part of the scientific method, which is a systematic approach to assessing theories through observations and determining the probability that a stated statement is true or false.

A good theory can make accurate predictions. For an analyst who makes predictions, hypothesis testing is a rigorous way of backing up his prediction with statistical analysis. It also helps determine sufficient statistical evidence that favors a certain hypothesis about the population parameter.