Definition: The null hypothesis is the default claim of no effect or no difference, stated as an equation about a parameter, which a significance test tries to find evidence against.
What is the null hypothesis?
Written H0, it is a statement such as “the population mean is 500” or “the proportion is 0.5.” It always contains an equals sign. The alternative hypothesis, Ha, says the parameter is less than, greater than, or different from that value.
How does the logic work?
Assume H0 is true, then measure how surprising your data would be. If very surprising, you reject H0. If not, you fail to reject it.
Worked example: a company claims its bulbs last 800 hours on average. You suspect less. Write H0: mu = 800 and Ha: mu < 800. A sample of 40 bulbs averaging 782 hours may or may not be surprising enough, depending on the spread.
What mistake is typical?
Saying you “accept” or “prove” the null. A test can only fail to find evidence against it. Mathbot’s wording: the data do not provide convincing evidence that the mean differs from 800.
Where to learn it
- Inference for Means with t Procedures – lesson
- Inference for Proportions: Intervals and Tests – lesson