The accompanying data on crack initiation depth (mm) was read from a lognormal probability plot that appeared in the article "Incorporating Small Fatigue Crack Growth in Probabilistic Life Prediction: Effect of Stress Ratio in Ti-6Al-2Sn-6Mo" (Intl. J. of Fatigue, 2013: 83-95). Although the pattern in the plot was quite straight, a normal probability plot of the data also shows a reasonably linear pattern. And a boxplot indicates that the distribution is quite symmetric in the middle 50% of the data and only mildly skewed overall. It is therefore reasonable to estimate and predict using t intervals.

a. Estimate the true average crack initiation depth with a 99% CI and interpret the resulting interval.
b. Predict the value of a single crack initiation depth by constructing a 99% PI.
c. Interpret in context the meaning of 99% in (b).

Transcribed Image Text:

4.7 5.1 5.2 5.3 5.6 5.86.36.7 7.2 7.4 7.78.5 8.9 9.310. 11.2