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Alternative Hypothesis

In hypothesis testing, there are two types of statistical hypothesis, Null hypothesis and alternative hypothesis. The null hypothesis, which is usually denoted by H0 is derived from the hypothesis that the sample observations will purely result from chance. The Alternative hypothesis, which is exactly the opposite of the null hypothesis is denoted by H1 or Ha, and denotes that the sample observations purely results from some random cause. In statistical testing, the researchers are interested in investigating a research problem. To evaluate the problem, they develop a prediction of the results referred to as the hypothesis or a ‘working statements’. The two working statements developed is the null and alternative hypothesis. The interest is proving whether the working statement (null hypothesis) is true or not.

How Alternative Hypothesis is applied

The alternative hypothesis is the opposite or alternative of null hypothesis. For instance, is the null hypothesis states that ‘Arsenal will win the cup’, then the alternative hypothesis states that ‘Arsenal will not win the cup’. This implies that the researchers is looking at whether there could be enough chances (with alternative hypothesis) to be able to reject or disagree with the null hypothesis.  Therefore, since the null and alternative hypotheses are contradictory, the researcher should examine whether there is enough evidence to reject the null hypothesis or not. If the null hypothesis is rejected, then it implies that the alternative hypothesis is accepted and vice versa. That is, ‘“reject H0” if the evidence supports alternative hypothesis, or “do not reject H0” or “decline to reject H0” if the evidence is insufficient to reject null hypothesis. This evidence is obtained from conducting a research on the sample data.

The mathematical symbols used in the alternative hypothesis as well as null hypothesis are shown below.

H0 (Null Hypothesis) Ha(Alternative Hypothesis)
equal (=) not equal (≠)
or greater than (>) or less than (<)
greater than or equal to (≥) less than (<)
less than or equal to (≤) more than (>)

Examples of Alternative Hypothesis in Research

  • A medical examination was conducted to investigate whether or not, the new medicine would reduce cholesterol by 25% in the body. State the  null and alternative hypothesis.

H0 (Null hypothesis): The medicine would reduce cholesterol by 25%

Ha (alternative hypothesis): The medicine would not reduce cholesterol by 25%

  • A university wants to find out whether the GPA of their students is different from 2.0 (out of 4.0). The null and alternative hypothesis would be stated as follows.

H0 (Null hypothesis): GPA of their students is not different from 2.0

Ha (alternative hypothesis): GPA of their students is different from 2.0