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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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You are testing the difference between high school freshmen and seniors on SAT performance. The null hypothesis is that the population mean SAT score of the seniors is equal to the population mean SAT score of the freshmen. You randomly sample 20 students in each grade and have them take the SAT. You find that the sample mean of the seniors is significantly higher than the sample mean of the freshmen. Which alternative hypothesis is accepted?

The population mean SAT score of the seniors is less than the population mean SAT score of the freshmen.

The population mean SAT score of the seniors is greater than the population mean SAT score of the freshmen.

You cannot be sure which alternative hypothesis to accept. You just know that the null hypothesis was rejected

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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