Informal Confidence Intervals — practice questions

Statistical Inference · Part 3 of 4

3 exam-style questions with model answers, plus 3 quick multi-choice questions — every question on this part of the standard, grouped by the 1 page of notes they come from.

Write a full answer before you reveal the model one. That comparison is where the learning happens.

Building an informal confidence interval

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AchievedShow

A random sample of $n = 25$ has median 40, $Q_1 = 32$ , $Q_3 = 52$ . Calculate the margin $E = 1.5 \times \text{IQR}/\sqrt{n}$ and give the confidence interval.

MeritShow

A sample of $n = 64$ eels has median length 48 cm, $Q_1 = 40$ , $Q_3 = 56$ . Build the informal confidence interval and interpret it in context.

ExcellenceShow

Two samples have the same median and IQR, but one has $n = 25$ and the other $n = 100$ . Explain, with the margins, how the sample size changes the interval and why that matters.

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