An article in the journal Neurology (1998, Vol. 50, pp. 1246–1252) observed that monozygotic twins share numerous physical, psychological, and pathological traits. The investigators measured an intelligence score of 10 pairs of twins. The data obtained are as follows:

Pair Birth Order: 1 Birth Order: 2 1 6.08 5.73 2 6.22 5.80 3 7.99 8.42 4 7.44 6.84 5 6.48 6.43 6 7.99 8.76 7 6.32 6.32 8 7.60 7.62 9 6.03 6.59 10 7.52 7.67

(a) Is the assumption that the difference in score is normally distributed reasonable?

(b) Find a 95% confidence interval on the difference in mean score. Is there any evidence that mean score depends on birth order?

(c) Test an appropriate set of hypotheses indicating that the mean score does not depend on birth order.