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Name: Assume a researcher has found a new type of gasoline that improves the
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Description: Assume a researcher has found a new type of gasoline that improves the gas mileage (MPG). He needs to figure out the effect of the new gasoline type with respect to the regular type. Suppose he selected 22 cars randomly and expected to carry out a co

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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Assume a researcher has found a new type of gasoline that improves the gas mileage (MPG). He needs to figure out the effect of the new gasoline type with respect to the regular type. Suppose he selected 22 cars randomly and expected to carry out a completely randomized design by taking 10 cars for new gasoline type and other 12 cars for regular gasoline type. Assume MPG is normally distributed for both types of gasoline.

Type

Sample Mean

( )

Sample standard deviation (s)

New Gasoline

Regular Gasoline

Assume that you need to conduct a hypothesis test to claim that the mean MPG of new gasoline is different than the mean MPG of regular.

What is the p-value of the test?

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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