Â Look again at the brain weight data in Display 9.31. This time, consider it a random sample taken from all animal species.
a. If you omit the three obvious outliers, you get the boxplot in Display 9.41. Has removing the three outliers improved the situation?
b. Construct the 95% confidence interval for the mean using the set of all 68 species. The summary statistics are 394.5 and s 1207.0. Then construct the 95% confidence interval for the mean with the three original outliers removed. The summary statistics are 149.4 and s 323.2.
c. How do the centers of the two confidence intervals in part b compare? The widths? What does this tell you about the sensitivity of confidence intervals to outliers?
d. If you take the natural log of each of the original 68 brain weights, you get the boxplot in Display 9.42 and these summary statistics: 2.977 and s 2.686. Construct and interpret a 95% confidence interval for the population mean on this transformed scale.