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Half Width and Number of Replications. Prefer smaller confidence intervals — precision Notation: Confidence interval: Half-width =. Want this to be “small,” say < h where h is pre-specified. Source: Systems Modeling Co. Half Width and Number of Replications (cont’d.).

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Half width and number of replications l.jpg
Half Width and Number of Replications

  • Prefer smaller confidence intervals — precision

  • Notation:

  • Confidence interval:

  • Half-width =

Want this to be “small,” say

< h where h is pre-specified

Source: Systems Modeling Co.


Half width and number of replications cont d l.jpg
Half Width and Number of Replications (cont’d.)

  • Can’t control t or s

  • Must increase n - how much?

  • Set half-width = h, solve for

  • Not really solved for n (t, s depend on n)

  • Approximation:

    • Replace t by z, corresponding normal critical value

Source: Systems Modeling Co.


Half width and number of replications cont d3 l.jpg
Half Width and Number of Replications (cont’d.)

  • Pretend that current s will hold for larger samples

  • Get

  • Easier but different approximation:

s = sample standard

deviation from “initial”

number n0 of replications

h0 = half width from “initial”

number n0 of replications

n grows quadratically as h decreases.

Source: Systems Modeling Co.