Adolescent obesity is a serious health risk affecting more than 5 million young people in the United States alone. Laparoscopic adjustable gastric banding has the potential to provide a safe and effective treatment. Fifty adolescents between 14 and 18 years old with a body mass index higher than 35 were recruited from the Melbourne, Australia, community for the study. Twenty-five were randomly selected to undergo gastric banding, and the remaining 25 were assigned to a supervised lifestyle intervention program involving diet, exercise, and behavior modification. All subjects were followed for two years. Ex21-48ADOBESE.jmp gives the weight losses, in kilograms, for the subjects who completed the study. a. Get the 5-number summaries and mean, s.d for each group. b. Without assuming the two groups having equal variances, give a 95% confidence interval for the mean weight loss difference between the gastric banding and intervention group. c. Test if gastric banding leads to greater weight loss than the lifestyle intervention program, give H0, Ha, test statistic, p-value, conclusion and 95% CI for the mean weight loss difference. d. Now assuming the two groups having equal variances, use the pooled two sample t procedures to redo the questions in (b) and (c).

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Q1: Adolescent obesity is a serious health risk affecting more than 5 million young people in the United States alone. Laparoscopic adjustable gastric banding has the potential to provide a safe and effective treatment. Fifty adolescents between 14 and 18 years old with a body mass index higher than 35 were recruited from the Melbourne, Australia, community for the study. Twenty-five were randomly selected to undergo gastric banding, and the remaining 25 were assigned to a supervised lifestyle intervention program involving diet, exercise, and behavior modification. All subjects were followed for two years. Ex21-48ADOBESE.jmp gives the weight losses, in kilograms, for the subjects who completed the study.

a. Get the 5-number summaries and mean, s.d for each group.

b. Without assuming the two groups having equal variances, give a 95% confidence interval for the mean weight loss difference between the gastric banding and intervention group.

c. Test if gastric banding leads to greater weight loss than the lifestyle intervention program, give H0, Ha, test statistic, p-value, conclusion and 95% CI for the mean weight loss difference.

d. Now assuming the two groups having equal variances, use the pooled two sample t procedures to redo the questions in (b) and (c).

Treatment
1 banding
banding
2
3
banding
4 banding
5 banding
6 banding
7 banding
8 banding
9 banding
10 banding
11 banding
12 banding
13 banding
14 banding
15 banding
16 banding
17 banding
18 banding
19 banding
20 banding
21 banding
22 banding
23 banding
24 banding
25 lifestyle
26 lifestyle
27 lifestyle
28 lifestyle
29 lifestyle
30 lifestyle
31
lifestyle
32 lifestyle
33 lifestyle
34 lifestyle
35 lifestyle
36 lifestyle
37 lifestyle
38 lifestyle
39 lifestyle
40 lifestyle
41 lifestyle
42 lifestyle
Loss
35.6
81.4
57.6
32.8
31
37.6
36.5
-5.4
27.9
49
64.8
39
43
33.9
29.7
20.2
15.2
41.7
53.4
13.4
24.8
19.4
32.3
2623
-3
20.6
11.6
15.5
-17
1.4
4
-4.6
15.8
34.6
6
-3.1
-4.3
-16.7
-1.8
-12.8

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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