Question 20A trucking firm is considering the installation of a new, low-restriction engine air filter for its long-haul trucks, but doesn’t want to make the switch unless the new filter can be shown to improve the fuel economy of these vehicles. A test is set up in which each of 10 trucks makes the same run twice once with the old filtration system and once with the new version. Given the sample results shown below, Truck NumberCurrent Filter(mpg)New Filter(mpg)17.67.324.17.2310.46.846.910.655.68.867.98.775.45.785.78.795.58.9105.37.1 Formulate the null and alternative hypotheses that can be used to decide whether the new filtration system could be superior. H0: the hypothesized mean is greater zero H0: the hypothesized mean is less than zero Ha: the hypothesized mean is less than zero Ha: the hypothesized mean is greater than zero

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Description: Question 20A trucking firm is considering the installation of a new, low-restriction engine air filter for its long-haul trucks, but doesn’t want to make the switch unless the new filter can be shown to improve the fuel economy of these vehicles. A t

Answered: Formulate the null and alternative…

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.7: Probability

Problem 58E: What is meant by the sample space of an experiment?

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Question 20

A trucking firm is considering the installation of a new, low-restriction engine air filter for its long-haul trucks, but doesn’t want to make the switch unless the new filter can be shown to improve the fuel economy of these vehicles. A test is set up in which each of 10 trucks makes the same run twice once with the old filtration system and once with the new version. Given the sample results shown below,

Truck Number	Current Filter (mpg)	New Filter (mpg)
1	7.6	7.3
2	4.1	7.2
3	10.4	6.8
4	6.9	10.6
5	5.6	8.8
6	7.9	8.7
7	5.4	5.7
8	5.7	8.7
9	5.5	8.9
10	5.3	7.1

Formulate the null and alternative hypotheses that can be used to decide whether the new filtration system could be superior.

		H0: the hypothesized mean is greater zero
		H0: the hypothesized mean is less than zero
		Ha: the hypothesized mean is less than zero
		Ha: the hypothesized mean is greater than zero

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 + ...

Expert Solution

Step 1

A test is set up in which each of 10 trucks makes the same run twice once with the old filtration system and once with the new version indicating that the paired t test is used.

Let $μ_{d}$ is the population mean difference between old filtration system and new filtration system. The claim of the test is that the new filtration system could be superior.

Null hypothesis:

$H_{0} : μ_{d} \geq 0$

That is, the hypothesized mean is greater zero.

Alternative hypothesis:

$H_{a} : μ_{d} < 0$

That is, the hypothesized mean is less than zero.

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