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Name: CarMD reports that the cost of repairing a hybrid vehicle is falling e
Uploaded: 2024-03-20T07:07:12.000Z
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Description: CarMD reports that the cost of repairing a hybrid vehicle is falling even while typical repairs on conventional vehicles are get-ting more expensive. The most common hybrid repair, replacing the hybrid inverter assembly, had a mean repair cost of $ 3

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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CarMD reports that the cost of repairing a hybrid vehicle is falling even while typical repairs on conventional vehicles are get-ting more expensive. The most common hybrid repair, replacing the hybrid inverter assembly, had a mean repair cost of $ 3,927 in 2012. Industry experts suspect that the cost will continue to de-crease given the increase in the number of technicians who have gained expertise on fixing gas– electric engines in recent months. Suppose a sample of 100 hybrid inverter assembly repairs completed in the last month was selected. The sample mean repair cost was $ 3,800 with the sample standard deviation of $ 500.

Is there evidence that the population mean cost is less than $ 3,927? (Use a 0.05 level of significance.)

Determine the p- value and interpret its meaning.

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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