Use a normal distribution test when the population standard deviation is known, and a t-test when is unknown and must be estimated using the sample standard deviation . In IB Mathematics: Applications and Interpretation HL, this choice applies regardless of sample size.
| Information available | Test distribution | Test statistic |
|---|---|---|
| Population standard deviation is known | Normal distribution | |
| Population standard deviation is unknown | t-distribution with degrees of freedom |
Also identify whether the alternative hypothesis requires a lower-tail, upper-tail, or two-tailed test. Enter the hypothesized mean, sample statistics, and sample size into the appropriate GDC test menu; calculator notation is acceptable as working, but the final response must use mathematical notation. The test assumes the sampled variable is normally distributed, with observations selected independently.
For example, suppose , , , and the claim is that the mean exceeds . Since is known, use the normal distribution:
The upper-tail p-value is . Since , reject . There is sufficient evidence at the significance level that the population mean exceeds .
A common misconception is that large samples automatically require the normal distribution. In AHL 4.18, the decisive issue is whether is known.
This is HL-only content from AHL 4.18: T and Z tests, Type I and Type II errors, suitable for GDC-active Papers 1, 2, or 3. Examiners expect hypotheses in terms of the population parameter , an explicit comparison between the p-value and , and a conclusion in context. Never say “accept ”; say “insufficient evidence to reject ” when the p-value is not significant.
