Answered: A study compared glucose levels among…

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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A study compared glucose levels among four age groups: toddlers, teenagers, adult, and seniors. The total sample size was n =30 (10 toddlers, 10 teenagers, 5 adult, and 5 seniors). A one-way analysis of variance was used to compare the population mean levels for the four age groups.

1. What are the numerator and denominator degrees of freedom for the F-test?

a. 10 for numerator and 30 for denominator.

b. None of the choices.

c. 4 for numerator and 30 for denominator.

d. 3 for numerator and 26 for denominator.

e. 3 for numerator and 29 for denominator.

2. The sum of squares for groups is SS Groups = 60. What is the Mean Square for groups (MS Groups)?

a. None of the choices.

b. 60

c. 20

d. 30

e. 15

3. The p-value for the F-test is = 0.02. Using the α = 0.05 significance level, what is the conclusion?

a. The null hypothesis is not rejected: the means are not significantly different.

b. The null hypothesis is not rejected: the means are significantly different.

c. The null hypothesis is rejected: the means are not significantly different.

d. The null hypothesis is rejected: the means are significantly different

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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