Problem 5. (20 points) In a random sample of 100 second-graders who are active in sports, the observed manual dexterity scores had the mean of 34.43 and the standard deviation of 3.55. Another (independent) random sample consisted of 100 second-graders who are not active in sports: in that sample, manual dexterity scores with mean 31.99 and standard deviation 4.46 were observed. a) Construct of a 99% confidence interval for the difference in population means based on the above data. What is your conclusion? b) Perform a hypothesis test in order to determine if there is sufficient evidence that second- graders who are active in sports have higher manual dexterity scores than those who are not active in sports. Use a =0.01. Clearly formulate your null and alternative hypotheses. In addition, report the p- value corresponding to this test. Is the conclusion consistent with the one you made in part a