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Name: Suppose you want to compare Mu_a and Mu_b, which are the true mean sto
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Description: Suppose you want to compare Mu_a and Mu_b, which are the true mean stopping distances for two different braking systems for cars travelling at 50 km/hr. An automobile manufacturer suspects Braking System A is more effective (has less stopping distanc

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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Suppose you want to compare Mu_a and Mu_b, which are the true mean stopping distances for two different braking systems for cars travelling at 50 km/hr. An automobile manufacturer suspects Braking System A is more effective (has less stopping distance) than Braking System B; that is, System A will stop a car travelling at 50 km/hr in a shorter distance, on average, than System B. In order to test the manufacturer's suspicion, what is the appropriate alternative hypothesis?

Select one:

H1: Mu_a – Mu_b < > 0

H1: Mu_a – Mu_b > 50

H1: Mu_a – Mu_b = 0

H1: Mu_a – Mu_b > 0

H1: Mu_a – Mu_b < 0

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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