• Explain how a confidence interval is related to a two-sided hypothesis test.

Confidence Interval – Hypothesis Testing

Confidence intervals contain a range of plausible estimates of the population parameter. Confidence intervals can also be used in hypothesis testing to assess whether a hypothesized population parameter falls within a certain range of values.

Let’s explore this idea of using a confidence interval for a hypothesis test!

Lego Structure Experiment^[1]

Picture a bridge made of Legos. One side has three support pieces, the others have two support pieces. How would you stabilize the bridge?

Most people would add a piece so that there are three supports on each side. But why not remove a piece so that each side has two supports instead? It turns out that getting people to subtract (whether a Lego block, ingredients in a recipe, or words in an essay) requires reminders and rewards.

In one experiment, the team offered [latex]197[/latex] people wandering around a crowded university quad a dollar to solve a puzzle. Participants viewed a Lego structure in which a figurine (represented by the piece of paper) was standing atop a platform with a large pillar behind her (see picture above). Atop that pillar, a single block in one corner supported a flat roof. Researchers asked the participants to stabilize the roof to avoid squashing the figurine. About half the participants were told: “Each piece you add costs [latex]10[/latex] cents.” Even with that financial penalty, only [latex]40[/latex] out of [latex]98[/latex] participants thought to remove the destabilizing block and just rest the roof on top of the wide pillar. The researchers gave the remaining participants a more explicit message: “Each piece you add costs [latex]10[/latex] cents, but removing pieces is free.” That cue prompted [latex]60[/latex] out of [latex]99[/latex] participants to remove the block.

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