Left ventricular mass (LVM), determined from echocardiograms, is an important risk factor for subsequent cardiovascular disease. The researchers are interested in assessing whether LVM changes in children over a 4-year period. To help plan the main study, a pilot study is conducted where echocardiograms are obtained from 10 random children from the Bogalusa Heart Study at baseline and after 4 years of follow-up. The sample mean of LVM change over the 4-year study period is 18.9 g and the sample standard deviation is 26.4 g. For answering the questions (a) and (b) below, assume that the sample variance of LVM change in this pilot study is the true variance of LVM change in the population.(a). If the expected increase in LVM is 10 g, what is the power of such a study if a two-sided test is to be used with α = 0.05? (b). Since this is a pilot study, the main question of interest is how many subjects would be needed to detect an increase of 10 g in mean LVM over 4 years using a two-sided test with α = 0.05 and power = 80%? Suppose the researchers also want to get an idea of the true population variance σ 2 of LVM change in children over a 4-year period based on the pilot data. (c). Perform a hypothesis test to assess whether σ 2 is significantly different from 300. Use both critical-value and p-value methods. (d). Find a 95% confidence interval (CI) of σ 2 . Is the result consistent with that of (c)? Justify your answer.