## 12.1 Confidence intervals

In a study of high strength--high ductile concrete (Ranade et al. 2015), the researchers 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 \(10\) s\({}^{-1}\), the \(n = 6\) concrete samples produced a **mean** first-crack strength of \(12.4\) MPa with a **standard deviation** of \(2.8\) MPa.

One student computes the approximate \(95\)% CI for the mean first-crack strength as \(12.4\pm 2.8\) 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 \(18.0\) 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.