Left ventricular mass (LVM) is an important risk factor for subsequent cardiovascular disease. A study is proposed to assess the relationship between childhood blood pressure levels and LVM in children as determined from echocardiograms. The goal is to stratify children into a normal bp group (

To help plan the main study, a pilot study 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.

(a) Provide a two-tailed p-value. (Use an approximate method if appropriate. Use = 0.05.)

State the null and alternative hypotheses (in g). (Enter != for as needed.)

(b) Find the test statistic. (If the test does not have a defined test statistic, enter DNE. Round your answer to two decimal places.)

(c) Use technology to find the p-value. (Round your answer to four decimal places.)

(d) Provide a 95% CI for 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.)

(e) Since this was 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 = 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.)

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