Answered: In a study of the birth order and…

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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In a study of the birth order and intelligence, IQ
tests were given to 18- and 19-year old men to
estimate the size of the difference, if any,
between the mean IQs of firstborn sons and
secondborn sons. The following data for 10
firstborn sons and 10 secondborn sons are
consistent with the means and standard
deviations necessary to conclude that the
samples come from populations that are
normally distributed.
Firstborn:
104 82 102 96 129 89 114 107 89 103

Secondborn:

103 103 91 113 102 103 92 90 114 113

a. Construct a 90% confidence interval for the
difference in mean IQ between firstborn and
secondborn sons.
b. Based on the confidence interval, is it reasonable
to believe that firstborn sons and secondborn sons may have the same mean IQ

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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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