Swimming Recently, a group of adults who swim regu-larly for exercise were evaluated for depression. It turned out that these swimmers were less likely to be depressedthan the general population. The researchers said thedifference was statistically significant. a) What does “statistically significant” mean in thiscontext?b) Is this an experiment or an observational study?Explain. c) News reports claimed this study proved that swim-ming can prevent depression. Explain why this conclu-sion is not justified by the study. Include an example of a possible lurking variable.d) But perhaps it is true. We wonder if exercise can wardoff depression, and whether anaerobic exercise (likeweight training) is as effective as aerobic exercise(like swimming). We find 120 volunteers not currentlyengaged in a regular program of exercise. Design anappropriate experiment.

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Swimming Recently, a group of adults who swim regu-
larly for exercise were evaluated for depression. It turned
out that these swimmers were less likely to be depressed
than the general population. The researchers said the
difference was statistically significant.
a) What does “statistically significant” mean in this
context?
b) Is this an experiment or an observational study?
Explain.
c) News reports claimed this study proved that swim-
ming can prevent depression. Explain why this conclu-
sion is not justified by the study. Include an example
of a possible lurking variable.
d) But perhaps it is true. We wonder if exercise can ward
off depression, and whether anaerobic exercise (like
weight training) is as effective as aerobic exercise
(like swimming). We find 120 volunteers not currently
engaged in a regular program of exercise. Design an
appropriate experiment.
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