WEIGHT LOSS EXAMPLE Being overweight may have many negative health consequences. A weight management professional developed a weight loss program involving careful attention to calories and regular exercise to help those who overweight. The program is designed to lower the weight of the participants. Nine people who are overweight were randomly selected to participate in the weight loss program. The participants were weighted before participating in the program. After the participants went through the weight loss program they were weighed again to see if the weight had decreased. Below is the data of the results. Data given: Patient Weight before Weight loss program Weight after Weight loss program A 150 148 B 220 221 C 175 170 D 200 200 E 300 295 F 290 293 G 285 282 H 195 194 I 295 292 Identify the hypotheses being tested: HINT: Small sample, we are testing the DIFFERENCE, We want to know if it is less than when AFTER - BEFORE. Basically we believe the weight loss program lowers the participant’s weight. Improvement means weight went down. Given: level alpha is 0.01. QUESTION: What is given? a) Population Mean: 234.44, Sample Mean: 232.78, Sample Standard Deviation: 2.69, Sample Size: 9 b) Population Mean: -1.67, Sample Mean: 0, Sample Standard Deviation: 2.69, Sample Size: 9 c) Population Mean: 0, Sample Mean: -1.67, Sample Standard Deviation: 2.69, Sample Size: 9 d) Population Mean: 232.78, Sample Mean: 234.44, Sample Standard Deviation: 2.69, Sample Size: 9

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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Question

WEIGHT LOSS EXAMPLE

Being overweight may have many negative health consequences. A weight management professional developed a weight loss program involving careful attention to calories and regular exercise to help those who overweight. The program is designed to lower the weight of the participants. Nine people who are overweight were randomly selected to participate in the weight loss program. The participants were weighted before participating in the program. After the participants went through the weight loss program they were weighed again to see if the weight had decreased. Below is the data of the results.

Data given:

Patient	Weight before Weight loss program	Weight after Weight loss program
A	150	148
B	220	221
C	175	170
D	200	200
E	300	295
F	290	293
G	285	282
H	195	194
I	295	292

Identify the hypotheses being tested: HINT: Small sample, we are testing the DIFFERENCE, We want to know if it is less than when AFTER - BEFORE. Basically we believe the weight loss program lowers the participant’s weight. Improvement means weight went down. Given: level alpha is 0.01.

QUESTION: What is given?

a) Population Mean: 234.44, Sample Mean: 232.78, Sample Standard Deviation: 2.69, Sample Size: 9

b) Population Mean: -1.67, Sample Mean: 0, Sample Standard Deviation: 2.69, Sample Size: 9

c) Population Mean: 0, Sample Mean: -1.67, Sample Standard Deviation: 2.69, Sample Size: 9

d) Population Mean: 232.78, Sample Mean: 234.44, Sample Standard Deviation: 2.69, Sample Size: 9

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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