The article "Mix Design for Optimal Strength Development of Fly Ash Concrete" (Cement and Concrete Research, 1989, Vol. 19, No. 4, pp. 634-640) investigates the compressive strength of concrete when mixed with fly ash (a mixture of silica, alumina, iron, magnesium oxide, and other ingredients). The compressive strength for nine samples in dry conditions on the twenty-eighth day are as follows (in megapascals) 40.2 30,4 28.9 30.5 224 25.8 18.4 14.2 15.3

(a) Given the following probability plot of the data, what is a logical assumption about the underlying distribution of the data?

(b) Find a 99% lower one-sided confidence interval on mean compressive strength. Provide a practical interpretation of this interval.

(c) Find a 98% two-sided confidence interval on mean com- pressive strength. Provide a practical interpretation of this interval and explain why the lower end-point of the inter- val is or is not the same as in part (b).

(d) Find a 99% upper one-sided confidence interval on the variance of compressive strength. Provide a practical in- terpretation of this interval.

(e) Find a 98% two-sided confidence interval on the variance of compression strength. Provide a practical interpretation of this interval and explain why the upper end-point of the interval is or is not the same as in part (d).

(f) Suppose that it was discovered that the largest observation 40.2 was misrecorded and should actually be 20.4.

Now the sample mean = 23 and the sample variance s' 39.8.

Use these new values and repeat parts

(c) and (e). Compare the original computed intervals and the newly computed intervals with the corrected observation value. How does this mistake affect the values of the sample mean, sample variance, and the width of the two-sided confidence intervals? (g) Suppose, instead, that it was discovered that the largest observation 40.2 is correct, but that the observation 25.8 is incorrect and should actually be 24.8.

Now the sample mean =25 and the standard deviations = 8.41.

Use these new values and repeat parts

(c) and (e). Compare the original computed intervals and the newly computed intervals with the corrected observation value. How does this mistake affect the values of the sample mean, the sample variance, and the width of the two-sided confi- dence intervals?

(h) Use the results from parts

(f) and (g) to explain the effect of mistakenly recorded values on sample estimates. Comment on the effect when the mistaken values are near the sample mean and when they are not.