12.1 Confidence intervals
In a study of high strength--high ductile concrete, Ranade et al. (2015) measured (among other things) the load required to create the first visible cracks in concrete samples under various strains rates.
Under a strain rate of \(10\,\text{s}^{-1}\), the \(n = 6\) concrete samples produced a mean first-crack strength of \(12.4\MPAs\) with a standard deviation of \(2.8\,\text{MPa}\).
One student computes the approximate \(95\)% CI for the mean first-crack strength as \(12.4\pm 2.8\,\text{MPa}\). Another student computes the approximate \(95\)% CI for the mean first-crack strength as \(12.4\pm (2\times 2.8)\), or from \(6.8\) to \(18.0\,\text{MPa}\).
- Both students are incorrect. Explain why the students are incorrect, and explain what they actually have calculated instead.
- Compute the correct (approximate) \(95\)% CI.
References
Ranade R, Li VC, Heard WF. Tensile rate effects in high strength-high ductility concrete. Cement and Concrete Research. 2015;68:94–104.