An article in Neurology (1998, Vol. 50, pp. 1246-1252) discussed that monozygotic twins share numerous physical, psychological, and pathological traits. The investigators measured an intelligence score of 10 pairs of twins, and the data follow: Pair Birth order: 1 Birth order: 2
1 6.08 5.73
2 6.22 5.8
3 7.99 8.42
4 7.44 6.84
5 6.48 6.43
6 6.32 8.76
7 7.6 6.32
8 6.03 7.62
9 7.52 6.59

Required:
a. Is the assumption that the difference in score is 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?