## 11.1 Confidence intervals

In a study of high strength–high ductile concrete (Ranade, Li, and Heard 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 10s$${}^{-1}$$, the $$n=6$$ concrete samples produced a mean first-crack strength of 12.4MPa with a standard deviation of 2.8MPa.

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, Ravi, Victor C. Li, and William F. Heard. 2015. “Tensile Rate Effects in High Strength-High Ductility Concrete.” Cement and Concrete Research 68: 94–104.