AI Tutor
Imagine you are handed three research problems: evaluating voter approval ratings, comparing battery lifespans from two competing brands, and checking if a new tire compound reduces braking distance on the same test car.
Each question requires a completely different statistical test, and choosing the wrong one invalidates your entire analysis.
How can you immediately tell which test fits any given scenario?

The Test Selection Decision Framework

Choosing the correct hypothesis test begins by identifying the Data Structure and number of samples, the variable type, and the parameter conditions.
A single-sample test evaluates whether a sample statistic differs significantly from a hypothesized population benchmark (such as ΞΌ=ΞΌ0\mu = \mu_0 or p=p0p = p_0).
What makes a problem a test of a proportion versus a test of a mean when numbers are involved in both?

Proportions vs. Means

A proportion test evaluates categorical binary data, where you count the number of 'successes' (xx) out of total trials (nn) to estimate a population rate pp.
A mean test evaluates quantitative measurements (such as mass, time, or temperature) to draw conclusions about the population average ΞΌ\mu.
For a single population mean ΞΌ\mu, when the population variance is known (Οƒ2\sigma^2) or the sample is large (nβ‰₯30n \ge 30) via the Central Limit Theorem, use a ZZ-test: Z=XΛ‰βˆ’ΞΌ0Οƒ/nZ = \frac{\bar{X} - \mu_0}{\sigma / \sqrt{n}}
When the population variance is unknown and estimated by the sample standard deviation ss in a small normal sample, use a Student's tt-test: t=XΛ‰βˆ’ΞΌ0s/nt = \frac{\bar{X} - \mu_0}{s / \sqrt{n}} with Ξ½=nβˆ’1\nu = n - 1 degrees of freedom.