c) Even if the difference is significant, why might the company choose to stick with regular gasoline'? d) Suppose you had done a "bad thing." (We're sure you didn't.) Suppose you had mistakenly treated these data as two independent samples instead of matched pairs. What would the significance test have found? Carefully explain why the results are so different. 6. Chapter 18: A Visual Analog Scale (VAS) is a graphic rating tool used to gauge relative intensity of subjective measures such as feelings, attitudes, or opinions. A VAS consists of a horizontal line which represents a continuous scale, typically from a zero value at left to a maximum value at right. The line is marked at intervals, which may or may not be assigned numerical values or descriptors such as "Never," "Seldom," "Sometimes," etc. Testers or subjects place an "x" or other mark on the line representing the location of their perceived rating or self-rating. The VAS shown below has been used to self-report pain intensity. For example, the pain intensity for the subject response below has a VAS value of 30. In an acupuncture study, 12 patients were randomly assigned to the acupuncture treatment and 8 to the placebo. The visual analog scale (VAS) was used to measure pain intensity before and after treatment for each patient in each treatment group. The following tables give the results of this simulated study. a. Is there sufficient evidence to conclude that acupuncture reduces pain intensity on average? b. Is there sufficient evidence to conclude that the acupuncture treatment produces a higher mean reduction in VAS scores compared to the placebo