1. Guinea Pig Lifetimes. Use the Welch t -tools to find a two-sided p-value and confidence inter- val for the effect of treatment on lifetimes of guinea pigs in Chapter 2, Exercise 11. Does the additive treatment effect seem like a sensible model for these data?
2. Schizophrenia Study. (a) Draw a histogram of the differences in hippocampus volumes in Display 4.12. Is there evidence that the population of differences is skewed? (b) Take the logarithms of the volumes for each of the 30 subjects, take the differences of the log volumes, and draw a histogram of these differences. Does it appear that the distribution of differences of log volumes is more nearly symmetric? (c) Carry out the paired t -test on the log-transformed volumes. How does the two-sided p-value compare with the one obtained on the untransformed data? (d) Find an estimate of and 95% confidence interval for the mean difference in log volumes. Back-transform these to get an estimate and confidence interval for the median of the population of ratios of volumes.