Answered: Given to dependent random samples with…

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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Given to dependent random samples with the following results:

Population 1: 83,72,64,61,72,74,72,66

Population 2: 85,64,66,52,78,83,70,68

Can it be concluded, from this data, that there is a significant difference between the two population means?

Let d= ( population 1 entry)-( population 2 entry), use a significance level of a = 0.05 for the test. Assume that both population are normally distributed.

1. State the null and alternative hypothesis for the test.

2. Find the value of the standard deviation of the paired differences. Round to one decimal place.

3. Commute the value of the test statistic. Round to three decimal places.

4. Determine the decision rule for rejecting the null hypothesis Ho. Round the numerical portion of your answer to three decimal places.

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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