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(d) 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 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.) 104 X subjects

(d) 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 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.) 104 X subjects

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 23PPS
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Please answer (d)

Cardiovascular Disease, Pediatrics 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 (< 80th percentile for their age, gender, and height) and an elevated bp group (≥ 90th percentile for their age, gender, and height) and compare change in LVM between the 2 groups. Before this can be done, one needs to demonstrate that LVM actually 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 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 1 2 3 4 5 6 7 8 9 10 Mean sd 4-year LVM (g) Baseline LVM (g) Change (g)* 162 127 141 97 110 107 166 83 78 173 124.4 34.8272 USE SALT 138 133 85 99 77 89 101 72 92 161 104.7 29.3600 24 -6 56 -2 33 18 65 11 -14 12 19.7 25.7555
Transcribed Image Text:Cardiovascular Disease, Pediatrics 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 (< 80th percentile for their age, gender, and height) and an elevated bp group (≥ 90th percentile for their age, gender, and height) and compare change in LVM between the 2 groups. Before this can be done, one needs to demonstrate that LVM actually 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 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 1 2 3 4 5 6 7 8 9 10 Mean sd 4-year LVM (g) Baseline LVM (g) Change (g)* 162 127 141 97 110 107 166 83 78 173 124.4 34.8272 USE SALT 138 133 85 99 77 89 101 72 92 161 104.7 29.3600 24 -6 56 -2 33 18 65 11 -14 12 19.7 25.7555
(d) 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 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.) 104 X subjects
Transcribed Image Text:(d) 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 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.) 104 X subjects
Expert Solution
Step 1

From the given information, we have

          Standard deviation sd , σ=25.7555

               Hypothesized mean, μ0=0

                              True mean, μ1=10

                                                    β=0.05

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