Answered: Jenny wants to compare the amount of…

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

Jenny wants to compare the amount of weight people lose at her gym using two popular, non-overlapping weight-loss programs, Shred It and Burn It. She randomly samples people who use each program and tracks their weight loss. Here is a summary of the results: Shred it Burn it Mean 11 kg 7 kg Standard deviation 3.5 kg 5.7 kg Number of people 35 45 1) From the above summary statistics, Jenny wants to test whether people using program “Shred it” have more weight loss averagely than the people who are using program “Burn it” by 2 kg. Conduct the hypothesis test at α=0.05. By technology, df=74. 2) Conduct a 95% confidence interval for the mean difference of weight loss using the two programs. Provide complete interpretation.

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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