Answered: A consumer group plans a comparative…

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 consumer group plans a comparative study of the mean life of four different brands of batteries. Ten batteries of each brand will be randomly selected and the time until the energy level falls below a pre-specified level is measured.

a) Which of the following is the appropriate alternative hypothesis for the null hypothesis: H₀: μ_a = μ_b = μ_c = μ_d? (In this problem, μ_a = mean time of Brand A, μ_b = mean time of Brand B, etc.)

H_a: none of the means are equal

H_a: μ_a ≠ μ_b ≠ μ_c ≠ μ_d

H_a: μ_a ≠ μ_b, μ_a ≠ μ_c, μ_a ≠ μ_d, μ_b ≠ μ_c, μ_b ≠ μ_d, μ_c ≠ μ_d

H_a: at least one of the means is different

b)In order to analyze the data with ANOVA, we need to satisfy the condition of randomization. How do we know that this condition has been met?

-One SRS of batteries is selected from a collection of batteries of all brands.

-The batteries are randomly allocated to the four brands.

-Separate random samples of batteries are selected from each brand.

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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