1. Yes, the passage states a correlation, here: â€œâ€¦those who felt they were paying lower rates than everyone else evaded only 12 percent of their tax, while those who felt they were paying more than everyone else evaded nearly one-third of their tax.â€ And here: â€œIn the laboratory, and perhaps in life, compliance walks hand in hand with the perception of fairness and equity.â€
Yes, the passage states or implies a claim about causation, here: â€œDestroy the [perception of fairness and equity], and whether there are penalties or not, compliance plunges.â€
Questions can be raised about whether U. Colorado undergraduates are representative of taxpayers in general. There is also no information about how many undergraduates participated. Questions can also be raised about whether perception of fairness and equity was the only or primary causal factor for evasion. For example, could the absolute value of taxes paid be a factor? Or, were there differences in the way in which participants in the different groups were told about their tax rates?

2. Yes, the passage states a correlation, here: â€œSurveying 1,000 post-operative patients recovering from knee-replacement surgery, it was discovered that fully 95 percent of them walked for less than 15 minutes per day.â€
Yes, the passage states or implies a claim about causation, here: â€œWe conclude, therefore, that walking can preserve the strength of oneâ€™s joints and avoid the need for surgery.â€
While the sample size of 1000 may be adequate, the studyâ€™s use of post-operative patients recovering from knee-replacement surgery is baffling; these patients were likely walking so little because they were recovering from knee-replacement surgery. If the passage is read more charitably and if it is assumed that the opening line refers to these post-operative patientsâ€™ level of walking historically prior to surgery, a little more credence could be given to the findings. However, there is no mention of the number of years any of the walkers walked less than or more than 15 minutes a day, or under what conditions; it seems reasonable to think that walking for more than 15 minutes a day, for years on end, on a hard warehouse floor, could cause the need for knee-replacement surgery.

3. Yes, the passage states a correlation, here: â€œThe prevalence of obesity among women who spent 21 hours or more watching television was 24 percent compared to just 11 percent for those who watched only a few hours a week.â€
Yes, the passage states or implies a claim about causation, but not directly between time spent watching television and obesity: â€œthere is a common cause underlying both heavy television watching and obesityâ€¦â€
The passage makes no mention of sample size or any other aspects of study design, so there is no way to evaluate the quality of this causal inductive argument in those terms. However, the study does not make the common mistake of too-quickly assuming or assigning causality between corollaries; instead, the study is sensibly conservative in considering the possibility that a third factor underlies the correlation observed.

Question1
3. Objectionable cause
Question2:
2. Confusing correlation and cause

Using the rules introduced so far, prove the following sequents: 1...