null hypothesis

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June 17, 2026

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A null hypothesis is a statistical assumption that is tested to be accepted or rejected in favor of an alternative. It specifically posits that any observed difference in data, such as between two sample means, is due to random chance rather than a systematic cause.1

In hypothesis testing, the null hypothesis (denoted H₀) is a tentative assumption about a population parameter. An alternative hypothesis (H_a) is then formulated, representing the opposite of the null hypothesis. Sample data is used to determine if the null hypothesis can be rejected. If rejected, the alternative hypothesis is considered true. For example, if a radio station assumes the average listener age is 30, the null hypothesis might be H₀: μ = 30, with the alternative being H_a: μ ≠ 30.2

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statistics
Hypothesis testing
This assumption is called the null hypothesis and is denoted by H₀. An alternative hypothesis (denoted H_a), which is the opposite of what is stated in the null hypothesis, is then defined. The hypothesis-testing procedure involves using sample data to determine whether or not H₀ can be rejected. If H₀…
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This assumption is called the null hypothesis and is denoted by H₀. An alternative hypothesis (denoted H_a), which is the opposite of what is stated in the null hypothesis, is then defined. The hypothesis-testing procedure involves using sample data to determine whether or not H₀ can be rejected. If H₀…
Read More

Student’s t-test
…usual first to formulate a null hypothesis, which states that there is no effective difference between the observed sample mean and the hypothesized or stated population mean—i.e., that any measured difference is due only to chance. In an agricultural study, for example, the null hypothesis could be that an application…
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…usual first to formulate a null hypothesis, which states that there is no effective difference between the observed sample mean and the hypothesized or stated population mean—i.e., that any measured difference is due only to chance. In an agricultural study, for example, the null hypothesis could be that an application…
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