Answered: To check the appeal of the packaging…

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

To check the appeal of the packaging design to men vs women, 100 male and 100 female volunteers rated the proposed design on a scale from 1 to 10. The mean rating of these males was 7.4 with a sample standard deviation of 1.5. The mean rating of these females was 8.0 with a sample standard deviation of 2.0. Let μ1 and μ2 represent the true mean ratings of these populations of men and women respectively. In testing the two-sided hypothesis

H0:μ1=μ2vs H0:μ1≠μ2

this data

a. is significant at both .01 and .05 levels.

b. is significant at the level a=0.01.

c. is significant at the level a=0.05.

d. is not significant at either the .01 or .05 levels.

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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