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An experiment was conducted to compare three types of paint for evidence of differences in their wearing qualities. They were exposed to abrasive action and the time in hours until abrasion was noticed was observed. Six specimens were used fer each type of paint. The data are as follows. L." .TE in - - H H .1 315 232i} 115 525 333 52:5 535 1T5 514 {a} Do an analysis of variance to determine if the evidence suggests that wearing quality differs for the three paints. Use a P-value in your conclusion. {o} If signicant differences are found, characterize what they are. Is there one paint that stands out? Discuss your ndings. is} Do whatever graphical analysis you need to determine ifassumptions used in {a} are valid. Discuss your ndings. (d) Suppose it is determined that the data for each treatment follow an exponential distribution. Does this suggest an attemative analysis? If so, do the altemalive analysis and give ndings. Four different locations in the northeast 1lilrere used for collecting ozone measurements in parts per million. Amounts of ozone 1were collected in 5 samples at each location. Location 1 2 3 4 0.00 0.15 0.10 0.10 0.10 0.12 0.13 0.0? 0.03 0.1T 0.00 0.05 0.03 0.10 0.00 0.03 0.11 0.14 0.00 0.00l {a} Is there sufcient information here to suggest that there are differences in the mean ozone levels across locations? Be guided by a Pvalue. [oi If signicant differences are found in {a}, characterize the nature of the differences. Use whatever methods 'fCIU have Ieamed. Group Project It is of interest to determine which tvpe of sports hall can be thmwn the longest distance. The comp-ehb'on involves a tennis ball, a baseball, and a softball. Divide the class into teams of ve individuals. Each team should design and conduct a separate experiment. Each team should also analyze the data from its own experiment. For a given team, each ofthe five individuals will throw each ball {after sufcient arm warmup]. The expen'mental response will be the distance {in feet} that the ball is thrown. The data for each team will involve 15 observations. Important points: {a} This is not a competition among teams. The competition is among the three tvpes of sports balls. One would expect that the conclusion drawn bv each team would be similar. {b} Each team should be gender mixed. {c} The experimental design for each team should be a randomized complete block design. The ve individuals thmwing are the blocks. {d} Be sure to incorporate the appropriate randomization in conducting the experiment. {e} The results should contain a description of the experiment with an ANDVA table complete with a Pvalue and appropn'ate conclusions. Llse graphical techniques where appropriate. Use multiple comparisons where appropriate. Draw practical conclusions concerning differences between the ball types. Be thorough. \fThe grades of a class of 9 students on a midterm report {x} and on the nal examination {1!} are as follows: ITIEIIITIHEIMMMGT F {3} Estimate the linear regression line. {b} Estimate the nal examination grade of a student who received a grade of 35 on the midterm report. The amounts of a chemical compound F that dissolved in 1oo grams of water at 1llarious temperatures 1 were recorded as follows: 15 12 10 ll 30 25 21 2:! d5 31 33 23- 30 dd. 35] :1? T5 d8 51 M {a} Find the equation of the regression line {b} Graph the line on a scatter diagram. {c} Estimate the amount Df chemical that 1will dissolve in 10D grams of water at 5U\" C. \f