To help plan the main study, a pilot studyr is conducted where echocardiograms are obtained from 10 random children at baseline and after 4 years of follow-up. The data are given in the table below. Pilot data on left ventricular mass (LVM) in children ID 4-year LVM (9) Baseline LVM (9) Change {g)* 1 164 138 26 2 125 133 -S 3 141 85 56 4 97 97 D 5 112 77 35 6 1-09 89 2D 7 166 103 63 8 83 72 11 9 78 94 -16 10 171 161 10 Mean 124.6 104.9 19.7 5d 34.5678 29.3009 25.9617 (a) What test can be used to assess if there is a change in mean LVM over 4 years? 'I' onesample ttest for the mean of a normal distribution one-sample inference for the Poisson distribution one-sample test for a binomial proportion one-sample ,152 test for the variance of a normal distribution one-sample 2 test for the mean of a normal distribution {b} Implement the test in Jart [a] and provide a two-tailed p-value. (Use an approximate method if appropriate. Use a = 0.05.} State the null and alternative hypotheses [in g). [Enter != for i as needed.) H: ,uzO O H1: ,ul =0 Find the test statistic. {If the test does not have a defined test statistic, enter DNE. Round your answer to two decimal places.)- .-/ Use technology to find the p-value. [Round your answer to four decimal places.) p-value = v State your conclusion. Reject H0. There is sufcient evidence to conclude that there was a change in mean LVM over 4 years. '12:? Fail to reject H0. There is insufficient evidence to conclude that there was a change in mean LVM over 4 years. {j Fail to reject H0. There is sufficient evidence to conclude that there was a change in mean LVM over 4 years. i} Reject H0. There is insufficient evidence to conclude that there was a change in mean LVM over 4 years. [c] Provide a 95% C1 or the change in LVM [in g} over 4 years based on the data in the table. [Enter your answer using interval notation. Round your numerical values to two decimal places.)- (1.13_.3s..27} g {d} Since this was a pilot study, the main question of interestis how many subjects would be needed to detect an increase of 10 gin mean LVM over 4 years using a two-sided test with a = 0.05 and power = 80%? (Hint: Assume that the estimated variance of change in LVM in the pilot study is the true variance of change in LVM. Round your answer up to the next whole number.)- x subjects