Exercise 2: Confidence Interval Widths at Three Confidence Levels — Possible Solution
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GIVEN
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SE = 10

STEP 1: WIDTH AT EACH CONFIDENCE LEVEL
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Width = 2 x z* x SE (the margin applies on both sides of the estimate)

  90%: width = 2 x 1.645 x 10 = 32.9
  95%: width = 2 x 1.96  x 10 = 39.2
  99%: width = 2 x 2.576 x 10 = 51.52

STEP 2: CONFIRMING THE TRADEOFF
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32.9 < 39.2 < 51.52

The widths increase in step with the confidence level, exactly
matching this chapter's own confidence-vs-width tradeoff: reaching a
higher level of confidence (99% vs 90%) requires casting a wider net,
since a narrower interval at the same underlying data would miss the
true value more often across repeated sampling.

WHY THIS WORKS AS AN ANSWER
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Each width is computed directly using this chapter's own critical
values and the same fixed SE, and the increasing pattern is explicitly
confirmed and tied back to this chapter's own tradeoff explanation
rather than left as an unexplained numeric result.