Definition: A hypothesis test, or significance test, uses sample data to decide whether there is convincing evidence against a null hypothesis about a population parameter.
What are the steps?
- State H0 and Ha with the parameter named.
- Check conditions: randomness, independence, and a suitable shape or sample size.
- Compute the test statistic and the p-value.
- Compare with the significance level and conclude in context.
What does one look like?
Worked example: a machine should fill cans to a mean of 500 mL. A random sample of n = 36 gives a mean of 512 mL and standard deviation 18 mL. Then t = (512 – 500)/(18/6) = 12/3 = 4.0 with 35 degrees of freedom.
The two-sided p-value is well below 0.001, so we reject H0. There is convincing evidence that the true mean fill differs from 500 mL.
What goes wrong?
Stopping at the number without a sentence in context. Another mistake is reading a small p-value as proof that the difference is large; it only says the data are unlikely under H0. Mathbot always writes the conclusion in plain words.
Example: n = 36, mean 512, s = 18 versus H0: mu = 500 gives t = 4.0