Original question written by FE Exam AI Prep from the public FE Civil exam specification. Before release, a solver model re-derived the answer twice from the question alone, without its answer key, and a critic model checked the result, and the arithmetic was re-run as an executable calculation. No licensed engineer reviews these questions. It is not an NCEES question and does not come from any NCEES practice exam. FE Exam AI Prep is an independent study tool and is not affiliated with, endorsed by, or sponsored by NCEES.
Standard Error of the Mean: FE Civil practice problem 6
A construction materials lab tests n = 9 concrete cylinders cast from a new ready-mix design. The sample mean 28-day compressive strength is 4250 psi and the sample standard deviation is 180 psi. For a two-sided 95% confidence interval on the true mean strength, the t-value for n - 1 = 8 degrees of freedom is t = 2.306. What is the upper limit of the 95% confidence interval for the true mean strength?
- A4665.1 psi
- B4111.6 psi
- C4388.4 psi
- D138.4 psi
Show the answer and worked solution
Answer: C — 4388.4 psi
Worked solution
- Step 1. Compute the standard error of the sample mean
SE = s/sqrt(n)
SE = 180/sqrt(9) = 180/3 = 60
Units: psi / dimensionless = psi - Step 2. Compute the margin of error using the given t-value
E = t*SE
E = 2.306*60 = 138.36
Units: dimensionless * psi = psi - Step 3. Add the margin of error to the sample mean for the upper confidence limit
CI_upper = xbar + E
CI_upper = 4250 + 138.36 = 4388.36
Units: psi + psi = psi - Step 4. Common traps
Using the sample standard deviation directly as the standard error, without dividing by the square root of the sample size, inflates the margin of error far beyond what nine test cylinders can support. Subtracting the margin of error from the sample mean instead of adding it produces the lower confidence limit rather than the upper limit the question requests. Reporting the margin of error alone, without adding it back to the sample mean, leaves a value far too small to represent an actual compressive strength.
Why the other choices are wrong
- Choice A
- This value uses the full sample standard deviation as the standard error itself, skipping the division by the square root of the sample size, which produces a margin of error far larger than nine independent test cylinders can support.
- Choice B
- This value applies the correct margin of error but subtracts it from the sample mean instead of adding it, which yields the lower confidence limit rather than the upper limit the question specifically requests.
- Choice D
- This value is only the margin of error term, t multiplied by the standard error, reported without adding it back to the sample mean, so it cannot represent an actual compressive strength value.