Answered: The senior Class of 2012 at Rancho High…

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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The senior Class of 2012 at Rancho High strongly believes
that they have better grades than their predecessors. The
class president, a Statistics student, calculates the mean
GPA for the 725 seniors to be 2.97 with a standard deviation

of 0.67. The Class of 2011 had a mean of 2.83 with a stand-
ard deviation of 0.81. Which of the following is correct?

A) The means should be compared with a one sample
t-test, using 2011’s mean as the null hypothesis.
B) The means should be compared using a two sample
t-test.
C) The means should be compared using a confidence
interval for the difference of means.
D) The means should be compared by a matched-pair
t-test on the mean difference in GPAs.
E) Inference is not necessary since the data are for both
populations.

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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