An article in Neurology (Vol. 50, 1998, pp. 1246–1252) describes a finding that monozygotic twins share numerous physical, psychological, and pathological traits. The investigators measured an intelligence score of 10 pairs of twins, and the data are as follows:
(a) Is the assumption that the difference in score in normally distributed reasonable? Show results to support your answer.
(b) Find a 95% confidence interval on the difference in mean score. Is there any evidence that mean score depends on birth order?
(c) It is important to detect a mean difference in score of one point, with a probability of at least 0.90. Was the use of 10 pairs an adequate sample size? If not, how many pairs should have been used?
