23-Ind-A6 Systems Simulation · December 2013

Question 4 of 14: Question 4 (Part B, Q2 — Required Sample Size for Firm B)

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

National Exams — December 2013 — 98-Ind-A6 Systems Simulation. Three-hour, closed-book exam; one of two permitted calculators (Sharp or Casio), one 8.5″×11.0″ aid sheet (both sides). Format: 14 sub-questions across four parts — Part A (do 1 of 2, 25 marks), Part B (do 3 of 5, 15 marks), Part C (do 1 of 3, 10 marks), Part D (do 2 of 4, 20 marks); 7 questions, 70 marks constitute a complete paper. All fourteen sub-questions are solved below for completeness (the source restarts its own numbering at 1 within each Part). Statistical tables (Normal, t, chi-square, F) were supplied with the exam; the values below are the same table values obtained by direct computation.

Reference texts: Banks, Carson, Nelson & Nicol, Discrete-Event System Simulation (5th ed., Pearson) — simulation study design, random-number generation, input/output data analysis, variance reduction, verification & validation, queueing simulation; Montgomery, Design and Analysis of Experiments (9th ed., Wiley) — factorial designs and ANOVA.

Question 4 (Part B, Q2 — Required Sample Size for Firm B) (5 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. Firm B's 10 pilot transit times (8, 9, 7, 18, 8, 12, 4, 5, 6, 11 days) give sample mean $\bar x_B = 8.8$ days and sample SD $s_B = 4.077$ days; the target precision is $E=\pm1$ day at a 19-in-20 (95%) confidence level.

Find. The total sample size $n$ needed so the 95% CI half-width on the mean transit time is $\le 1$ day.

Approach. Use the standard sample-size-for-a-mean formula, treating the pilot SD as the working estimate of $\sigma$.

Sample-size formula. For a 95% CI ($Z_{0.975}=1.960$) with half-width $E$: $$n = \left(\frac{Z_{0.975}\,s_B}{E}\right)^2 = \left(\frac{1.960\times 4.077}{1}\right)^2 = 63.85.$$
Round up. Sample size must be an integer that meets or exceeds the target, so $$n = \lceil 63.85\rceil = \boxed{64\ \text{observations, total}}.$$
Additional data to collect. Angus already has 10 pilot observations, so he needs $64-10=\boxed{54\ \text{more}}$.

Quantity	Result
Working SD estimate ($s_B$)	4.077 days
Required total sample size	64
Additional samples beyond the pilot 10	54

Check: uses the pilot-study SD as a plug-in estimate of $\sigma$ (the standard practical approach when $\sigma$ is unknown) rather than a $t$-based iterative size, which is accurate enough once $n$ is this large.

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