The Null Names One Curve, and x-bar Is Not a Hypothesis

You'll learnhow to state hypotheses about a population mean before any computation, why the null must carry equality and the alternative must take its direction from the research question, how a paired design changes the parameter to a mean difference, and why the procedure is t.

A manufacturer promises its batteries last 128 hours on average. A consumer group can afford to test 25 of them, and those 25 come back at 124.6. This animation draws the curve that promise actually names — where sample means of 25 would land if it were true — and marks the 124.6 in its tail. Then it breaks each setup rule in turn and shows the price on screen: move the null's center to 130 and the tail past the same data falls from 0.038 to 0.004; pick the direction after peeking and both five percent tails light up, so a five percent test is quietly spending ten. It finishes with the paired version, where twelve students measured twice give twelve differences and eleven degrees of freedom, and with the reason every one of these tests is t rather than z. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · HYPOTHESES ABOUT mu · ONE NULL CURVE · PAIRED SETUP · v2

One curve, one null value, a direction fixed in advance, and a cutoff that is t.

Before you start

What you're looking at

An hours axis. The curve is where sample means of 25 batteries would land if the maker's claim of 128 hours were true.

The question

The 25 tested came back at 124.6. What has to be written down, before any of that number is used?

Step 1 / 12