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 $10$ 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.