Answered: 4. A new vitamin supplementation…

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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4.
A new vitamin supplementation program is intended to decrease average resting heart rate in
individuals at risk for hypertension. Assume that a team of researchers are hopeful that resting
heart rate in their population will get down to less than 68 bpm, in a population with a standard
deviation of 2 bpm. In order to test this goal reduction, the team gathers a SRS of 273
participants in their program and calculates a sample average resting heart rate of 74 bpm.
A) Carry out a one sample Z test to determine if the team can conclude that the supplementation
program is successful in meeting their goal reduction in resting heart rate. Use an α=0.05.
B) Construct a 95% Confidence interval about the sample mean, and interpret the result.

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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