The phrase ‘‘You dirty rat” does rats a disservice. In a recent study, rats showed compassion that surprised scientists. Twenty-three of the 30 rats in the study freed another trapped rat in their cage, even when chocolate served as a distraction and even when the rats would then have to share the chocolate with their freed companion. (Rats, it turns out, love chocolate.) Rats did not open the cage when it was empty or when there was a stuffed animal inside, only when a fellow rat was trapped. We wish to use the sample to estimate the proportion of rats to show empathy in this way. The data are available in the dataset Compassionate Rats.
(a) Give the relevant parameter and its point estimate.
(b) Describe how to use 30 slips of paper to create one bootstrap statistic. Be specific.
(c) Use StatKey or other technology to create a bootstrap distribution. Describe the shape and center of the bootstrap distribution. What is the standard error?
(d) Use the standard error to find and interpret a 95% confidence interval for the proportion of rats likely to show empathy.