02 25 Points A group of 64 randomly selected students have a mean score of 38.6 with a standard deviation of 4.9 on a placement test. (a) What is the 90% condence interval for the mean score, u, of all students taking the test? Round your answer to one decimal place. (b) Interpret your interval above in terms of the problem. (c) Does you interval support that students score more than a 38 on the placement test? Explain. (d) How many students should we sample if we want to be 95% confident the true mean score is within 1 point? 03 35 Points An article in a journal reports that 34% of American fathers take no responsibility for child care. A researcher claims that the figure is higher for fathers in the town of Littleton. A random sample of 234 fathers from Littleton yielded 96 who did not help with child care. Test the researcher's claim at the 0.05 significance level. (a) State the null and alternative hypothesis and mark the claim. (b) Calculate and interpret the test statistic. Round your value to 2 decimal places. (c) Calculate and interpret the p-value. Provide a sketch and show your work. (d) State your decision. (e) Provide a conclusion in terms of the