When two ideas meet

Two people, one decision each time. Choose, see what actually happens, then reflect.

A case · you decide

Samira and Dev: how much sample averages wobble

Samira & Dev — a student who thinks about many possible samples, and a friend who knows the shape their averages make

The idea in play: averages of random samples cluster around the true mean with spread σ/√n, so larger samples give steadier averages.

Test scores at a school have a standard deviation of 10 points. Samira keeps drawing random samples of 25 students and writing down each sample's average.

Dev explains that the averages will pile into a bell shape around the true mean.

How spread out are the sample averages?

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A case · you decide

Lena and Tomas: an interval that leaves out zero

Lena & Tomas — a student who reports honest ranges, and a friend who runs hypothesis tests

The idea in play: a 95% confidence interval that does not contain zero corresponds to rejecting “no difference” at the 5% level.

A study compares two study methods. The 95% confidence interval for the difference in average scores is 1.2 to 4.8 points.

Tomas's null hypothesis is that the true difference is zero.

What does the interval say about Tomas's test?

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