due by midnight cst. thank you!
Q20-24 Project Farm is a Youtube channel that routinely compares different products. In one episode, the channel evaluated different options for loosening rusty bolts. Eight options were evaluated, including a control group where no treatment was given ("none" in the graph), to determine which was most effective. For all treatments, there were four bolts tested, except for a treatment of heat with a blow torch, where only two data points were collected. The results are shown in the figure below: Heat 7 WD-40 Royal Purple PB Blaster- Liquid Wrench AeroKroil - Acetone/ATF - none - 90 100 110 120 130 140 Torque Required to Loosen Rusty Bolt, in Foot-Pounds Below is the ANOVA output for the data. Df Sum Sq Mean Sq F value Pr(>F) treatment 7 3603.43 514.78 4.03 0.0056 Residuals 22 2812.80 127.85 20. True or False: The hypotheses are below are valid: Ho: The torque required does not, on average, differ among the different treatments. HA: Some methods make it easier or more difficult to loosen a bolt (requiring less torque), on average. 21. True or False: The p-value of 0.0056 is smaller than 0.05, so we would fail to reject HO. That is, there is no evidence that at least some of the methods perform better or worse than others at reducing the torque required to loosen rusty bolts. 22. The table below are p-values for pairwise t-tests comparing each of the different groups. These p-values have not been corrected for multiple comparisons. With 28 pairs, what would be the correct Bonferroni correction to the default significance level of a =0.05? a. 0.01 b. 0.1 c. 0.005 d. 0.00179 Aerokroil Heat Liquid Wrench none PB Blaster Royal Purple WD-40 Acetone/ATF 0.2026 0.0308 0.0476 0. 1542 03294 0.5222 0.3744 AeroKroil 0.0027 0.0025 0.8723 0.7551 0.5143 0.6883 Heat 0.5580 D.0020 D.0050 D.0096 0.0059 Liquid Wrench 0.0017 0.0053 0.0117 0.0065 none 0.6371 0.4180 0.5751 PB Blaster 0.7318 0.9286 Royal Purple 0.8000 23. Which pair of groups appears most likely to represent a difference using the Bonferroni correction from Question 22? a. none vs Liquid Wrench b. Royal Purple vs. Heat c. WD-40 vs AeroKroll d. PB Blaster vs Heat 24. True or False: We can conclude that Liquid Wrench did in fact help reduce the torque required vs doing nothing. That said, we cannot confidently say Liquid Wrench was any better than any of the other methods