Curing concrete is known to be vulnerable to shock vibrations, which may cause cracking or hidden damage to the material. As part of a study of vibration phenomena, the paper "Shock Vibration Test of Concrete" (ACI Materials J., 2002: 361-370) reported the accompanying data on peak particle velocity (mm/sec) and ratio of ultrasonic pulse velocity after impact to that before impact in concrete prisms.

Transverse cracks appeared in the last 12 prisms, whereas there was no observed cracking in the first 18 prisms.
a. Construct a comparative boxplot of ppv for the cracked and uncracked prisms and comment. Then estimate the difference between true average ppv for cracked and uncracked prisms in a way that conveys information about precision and reliability.
b. The investigators fit the simple linear regression model to the entire data set consisting of 30 observations, with ppv as the independent variable and ratio as the dependent variable. Use a statistical software package to fit several different regression models, and draw appropriate inferences.

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bs pp RatioObs Ratio 1 160 996 16 708990 2 164 996 17806 984 178 999 8 884 986 19 526 .991 5 293.993 20 490 993 6 289 .997 21 598 .993 415 999 22505 993 8 478 .997 23 525 .990 24 675 .991 4 252 997 0 3992 10 486 985 25 1211 981 20 1036 986 995 27 000984 13 749 994 28 151 982 14 772 994 29 144 962 30 1068 986 11 604 12 995 528 15 532 987