Answered: A study is conducted to compare two…

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

A study is conducted to compare two brands of paint. A consumer testing service found the following
summary statistics using two samples of four 1-gallon cans of each brand.

The consumer testing service wants to test the hypothesis the population mean coverage of brand A is
significantly different from the population mean coverage of brand B.

What is the null hypothesis?

Transcribed Image Text:Sample size Sample mean coverage (square feet) Sample standard deviation (square feet) Brand A n₁ = 4 x₁ = 546 S₁ = 31 Let μ₁ be the population mean coverage of brand A M1 μ₂ be the population mean coverage of brand B Brand B n₂ = 4 = 492 x2 S₂ = 26

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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