NETMaths
The bookUnit 4 · Hypothesis Testing79 / 83

Likelihood ratio and standard tests

Why this is asked: Match the situation to the test and remember the degrees of freedom. For confidence intervals, watch whether the quantile is upper or lower and whether σ is known.

Standard tests and confidence intervals

The written notes for this page come with the Notes pack. The video, the visual and the practice below are free.

See pricing

See it move

What 95% confidence actually meansinteractive

Forty samples, forty intervals, and a count of how many cover the truth — the misconception this kills is worth several marks.

Unlock interactive visuals

The trap here

“Any interval of the form [Xˉ(S/n)t,)[{\bar{X}} - (S/\sqrt{n})t, \infty) with a 90% quantile t is a 90% confidence interval” — false

t = tn1,0.9t_{n-1,0.9} under the convention tm,αt_{m,\alpha} =(1α)= (1-\alpha)-th quantile

That t is the 10th percentile, so the interval has coverage 10%, not 90%.

More on this →

Next: Gauss–Markov, regression, ANOVA basics

Create a free account to keep your place and have this feed your study plan.

Open this in the full syllabus view · Unit 4