Exercises 3.71 to 3.73 consider the question (using fish) of whether
uncommitted members of a group make it more democratic. It has been argued
that individuals with weak preferences are particularly vulnerable to a vocal
opinionated minority. However, recent studies, including computer simulations,
observational studies with humans, and experiments with fish, all suggest that
adding uncommitted members to a group might make for more democratic decisions
by taking control away from an opinionated minority. \({ }^{36}\) In the
experiment with fish, golden shiners (small freshwater fish who have a very
strong tendency to stick together in schools) were trained to swim toward
either yellow or blue marks to receive a treat. Those swimming toward the
yellow mark were trained more to develop stronger preferences and became the
fish version of individuals with strong opinions. When a minority of five
opinionated fish (wanting to aim for the yellow mark) were mixed with a
majority of six less opinionated fish (wanting to aim for the blue mark), the
group swam toward the minority yellow mark almost all the time. When some
untrained fish with no prior preferences were added, however, the majority
opinion prevailed most of the time. \({ }^{37}\) Exercises 3.71 to 3.73
elaborate on this study.
Training Fish to Pick a Color Fish can be trained quite easily. With just
seven days of training, golden shiner fish learn to pick a color (yellow or
blue) to receive a treat, and the fish will swim to that color immediately. On
the first day of training, however, it takes them some time. In the study
described under Fish Democracies above, the mean time for the fish in the
study to reach the yellow mark is \(\bar{x}=51\) seconds with a standard error
for this statistic of 2.4 . Find and interpret a \(95 \%\) confidence interval
for the mean time it takes a golden shiner fish to reach the yellow mark. Is
it plausible that the average time it takes fish to find the mark is 60
seconds? Is it plausible that it is 55 seconds?
