6. The accompanying data on crack initiation depth (um) 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-6AI-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. 4.7 5.1 5.2 5.3 5.6 5.8 6.3 6.7 7.2 7.4 7.7 8.5 8.9 9.3 10.1 11.2 (a) Check that the conditions for our t procedures are satisfied. (b) Estimate the true average crack initiation depth with a 99% CI and interpret the resulting interval.

Question

Probability and statistics. Please answer part (a)

6. The accompanying data on crack initiation depth (um) 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-6AI-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.
4.7 5.1 5.2 5.3 5.6 5.8 6.3 6.7
7.2 7.4 7.7 8.5 8.9 9.3 10.1 11.2
(a) Check that the conditions for our t procedures are satisfied.
(b) Estimate the true average crack initiation depth with a 99% CI and interpret the resulting interval.

Image Transcription

6. The accompanying data on crack initiation depth (um) 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-6AI-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. 4.7 5.1 5.2 5.3 5.6 5.8 6.3 6.7 7.2 7.4 7.7 8.5 8.9 9.3 10.1 11.2 (a) Check that the conditions for our t procedures are satisfied. (b) Estimate the true average crack initiation depth with a 99% CI and interpret the resulting interval.

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