3. {15 points] Researchers at University of Wisconsin-Point Place1 are interested in developing ways to increase the spatialtemporal reasoning of preschool children, an ability to visual- ize spatial patterns and mentally manipulate them over a time-ordered sequence of spatial transformations. The researchers want to design a study to evaluate which of several methods proposed to accelerate the growth in spatialtemporal reasoning yields the greatest increase in a child's development in this area. There are 3 methods proposed: taking piano lessons for 3 months, playing specially developed computer video games for 3 months, and playing specially designed games in small groups supervised by a trained instructor. The researchers measure the effectiveness of the three programs by assessing the children and assigning each one a reasoning score both before and after participation in the program. The difference in these two scores is the response variable. A control group is also included to measure the change in reasoning for children not given any special instruction. The researchers conduct a study involving 95 students. 24 students are randomly assigned to each of the 4 instructional conditions. The data are given in the data set child. 1There is no place named Point Place in Wisconsin. It is made up from the sitoom That '705 Show. 3 (a) Use a = 0.05 to test the hypothesis that there is a difference in the effectiveness means of the methods of instruction. Show the ANOVA table and make the conclusion. [Hint]: You may need to rearrange the data set so that it can be correctly read by R functions such as lmO, aovov etc.,'; points] (b) With or = 0.04, apply the Bonferroni method to conduct ad-hoc pairwise multiple com- parisons. Include all pairwise condence intervals and conclude that which pairs of population means are signicantly different. M points] [c] With at = 0.04, apply the Tukest HSD method to conduct ad-hoc pairwise multiple comparisons. Include all pairwise condence intervals and conclude that which pairs of population means are signicantly different. M points] (d) Comparing (b) and (c), which method is more conservative, i.e., having wider pairwise condence intervalsw' points}