It has been hypothesized that children's performance on a particular test of spatial ability will improve significantly between the ages of 10 and 12. To test this hypothesis, eight 10-year-old children are given the spatial ability test and then, two years later as 12-year- olds, are given the same test a second time. The following data were obtained: Children 10-year-old scores 12-year-old scores 1 20 28 2 32 34 3 26 27 4 36 40 5 18 28 6 25 24 7 30 34 8 16 21 a) Are the children's spatial ability scores as 12-year-olds significantly higher than they were at 10 years of age (alpha = .005)? (10 points) b) Is the variance of the children's scores as 10-year-olds significantly different from 68.5: the typical population variance (alpha = .05)? (10 points)