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(b) Implement the test in part (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 as needed.) Ho: H₂: 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= State your conclusion. Reject Ho. There is insufficient evidence to conclude that there was a change in mean LVM over 4 years. O Reject Ho. There is sufficient evidence to conclude that there was a change in mean LVM over years. Fail to reject Ho. There is insufficient evidence to conclude that there was a change in mean LVM over 4 years. Fail to reject Ho. There is sufficient evidence to conclude that there was a change in mean LVM over 4 years. (c) Provide 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.) 9 (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.) subjects

(b) Implement the test in part (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 as needed.) Ho: H₂: 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= State your conclusion. Reject Ho. There is insufficient evidence to conclude that there was a change in mean LVM over 4 years. O Reject Ho. There is sufficient evidence to conclude that there was a change in mean LVM over years. Fail to reject Ho. There is insufficient evidence to conclude that there was a change in mean LVM over 4 years. Fail to reject Ho. There is sufficient evidence to conclude that there was a change in mean LVM over 4 years. (c) Provide 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.) 9 (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.) subjects

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.5: Correlation And Causation
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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 4-year LVM (g) Baseline LVM (g) Change (g)* 1 2 3 4 5 6 7 8 9 10 Mean sd 162 127 141 95 110 109 166 81 78 173 124.2 35.1720 138 133 87 97 77 89 103 74 92 161 105.1 29.0036 24 -6 54 -2 33 20 63 7 -14 12 19.1 25.2342
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 4-year LVM (g) Baseline LVM (g) Change (g)* 1 2 3 4 5 6 7 8 9 10 Mean sd 162 127 141 95 110 109 166 81 78 173 124.2 35.1720 138 133 87 97 77 89 103 74 92 161 105.1 29.0036 24 -6 54 -2 33 20 63 7 -14 12 19.1 25.2342
0.05.) (b) Implement the test in part (a) and provide a two-tailed p-value. (Use an approximate method if appropriate. Use α = State the null and alternative hypotheses (in g). (Enter != for ‡ as needed.) Ho: H₁: 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 = State your conclusion. O Reject Ho. There is insufficient evidence to conclude that there was a change in mean LVM over 4 years. O Reject Ho. There is sufficient evidence to conclude that there was a change in mean LVM over 4 years. Fail to reject Ho. There is insufficient evidence to conclude that there was a change in mean LVM over 4 years. Fail to reject Ho. There is sufficient evidence to conclude that there was a change in mean LVM over 4 years. (c) 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.) g (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.) subjects
Transcribed Image Text:0.05.) (b) Implement the test in part (a) and provide a two-tailed p-value. (Use an approximate method if appropriate. Use α = State the null and alternative hypotheses (in g). (Enter != for ‡ as needed.) Ho: H₁: 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 = State your conclusion. O Reject Ho. There is insufficient evidence to conclude that there was a change in mean LVM over 4 years. O Reject Ho. There is sufficient evidence to conclude that there was a change in mean LVM over 4 years. Fail to reject Ho. There is insufficient evidence to conclude that there was a change in mean LVM over 4 years. Fail to reject Ho. There is sufficient evidence to conclude that there was a change in mean LVM over 4 years. (c) 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.) g (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.) subjects
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Given that a pilot study is conducted where echocardiograms are obtained from 10 random children at baseline and four-year follow-up as

ID 4-year LVM (g) Baseline LVM (g) Change (g)*
1 162 138 24
2 127 133 -6
3 141 87 54
4 95 97 -2
5 110 77 33
6 109 89 20
7 166 103 63
8 81 74 7
9 78 92 -14
10 173 161 12
Mean 124.2 105.1 19.1
sd 35.17196 29.00364 25.23424

 

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