Answered: After the battery times were measured,…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 31EQ

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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.

Transcribed Image Text:Y Brigham Young University 8 BYU Learning Suite Y Quiz: Credit Quiz 30A (1 unread) - mckayballstaedte X b Verify Email | bartleby + A byu.instructure.com/courses/7512/quizzes/174025/take After the battery times were measured, the following dotplots were obtained. On the basis of these dot plots, is the condition of normality of populations met? Brand D : : Brand C Brand B Brand A 40 45 50 55 Time O No, because the sample sizes were not big enough to apply the Central Limit Theorem. O Yes, because each of the populations are known to be normally distributed. O Yes, because the dot plots show no outliers. O No, because at least one of the dot plots shows some outliers. 12:22 PM P Type here to search 45 O G 4) 11/16/2020

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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