## 12.1 Confidence intervals

In a study of high strength--high ductile concrete , 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.

1. Both students are incorrect. Explain why the students are incorrect, and explain what they actually have calculated instead.
2. 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.