Schizophrenia is believed to cause changes in dopamine levels. Twenty-five patients with schizophrenia were classified as psychotic or non-psychotic after being treated with an antipsychotic drug. Samples of cerebral fluid were taken from each patient and assayed for dopamine b-hydroxylase (DBH) activity. The dopamine measurements for the two groups are in nmol/(ml)(h)/(mg) of protein and are stored in the data frame Schizo as well as in the following table (Sternberg et al., 1982).
(a) Construct side-by-side boxplots of the two groups. Based on the boxplots, comment on the relative shapes of the two distributions.
(b) Construct quantile-quantile plots for the two groups, and comment on whether or not the plots support the analysis in part (a).
(c) Construct a 95% confidence interval for the true ratio of psychotic to non-psychotic variances.
(d) Based on the confidence interval for the ratio of variances, should the variances be pooled to construct a 95% confidence interval for the true dopamine level difference between psychotic and non-psychotic patients?
(e) Construct a 95% confidence interval for the true dopamine level difference between psychotic and non-psychotic patients.
(f) Does the confidence interval contain zero? What does this say about the effectiveness of the antipsychotic drug?