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 x̅ = 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?

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. 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 groupswam 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.