Exercise 2: Standard Error at Three Sample Sizes — Possible Solution
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GIVEN
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sigma = 80

STEP 1: STANDARD ERROR AT EACH SAMPLE SIZE
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Per this chapter's own SE = sigma/sqrt(n) formula:

  n = 4:  SE = 80 / sqrt(4)  = 80 / 2  = 40
  n = 16: SE = 80 / sqrt(16) = 80 / 4  = 20
  n = 64: SE = 80 / sqrt(64) = 80 / 8  = 10

STEP 2: THE PATTERN
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Going from n=4 to n=16 (a 4x increase in sample size) halves the
standard error, from 40 to 20. Going from n=16 to n=64 (again a 4x
increase) halves it again, from 20 to 10. In both cases, the sample
size had to QUADRUPLE to cut the standard error in half - the exact
same pattern Probability & Statistics Fundamentals' own Chapter 8
demonstrated with a different sigma value, confirming this isn't a
coincidence specific to one example but a direct consequence of the
square root in the SE = sigma/sqrt(n) formula itself: halving SE
requires sqrt(n) to double, which requires n to increase by a factor
of 2^2 = 4.

WHY THIS WORKS AS AN ANSWER
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Each standard error is computed directly from this chapter's own
formula, and the pattern is identified by comparing consecutive
results and explicitly tracing it back to the same square-root
mechanism already established in the sibling course, rather than
treating it as a new, unrelated observation.