Answered: Suppose you want to test the claim the…

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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Question

Suppose you want to test the claim the the paired sample data given below come from a population for which the mean difference is ??=0μd=0.

??6780788963596063568990768071x67786360569080y80895963897671

Use a 0.050.05 significance level to find the following:
(a)    The mean value of the differnces ?d for the paired sample data
?⎯⎯⎯=d¯=
(b)    The standard deviation of the differences ?d for the paired sample data
??=sd=
(c)    The t test statistic
?=t=
(d)    The positive critical value
?=t=
(e)    The negative critical value
?=t=
(f)    Does the test statistic fall in the critical region?

A. No
B. Yes

(g)    Construct a 9595% conficence interval for the population mean of all differences ?−?x−y.
<??<<μd<

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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