Answered: sample of colored candies was obtained…

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 #6

A sample of colored candies was obtained to determine the weights of different colors. The ANOVA table is shown below. It is known that the population distributions are approximately normal and the variances do not differ greatly. Use a 0.025significance level to test the claim that the mean weight of different colored candies is the same. If the candy maker wants the different color populations to have the same mean weight, do these results suggest that the company has a problem requiring corrective action?

Source:	DF:	SS:	MS:	Test Stat, F:	Critical F:	P-Value:
Treatment:	8	0.072	0.009	1.2282	2.3529	0.2934
Error:	81	0.567	0.007
Total:	89	0.639

Should the null hypothesis that all the colors have the same mean weight be rejected?

A. No, because the P-value is greater than the significance level.

B. No, because the P-value is less than the significance level.

C. Yes, because the P-value is greater than the significance level.

D. Yes, because the P-value is less than the significance level.

Does the company have a problem requiring corrective action?

A. Yes, because it is likely that the candies do not have equal mean weights.

B. No, because it is not likely that the candies do not have equal mean weights.

C. No, because it is likely that the candies do not have equal mean weights.

D. Yes, because it is not likely that the candies do not have equal mean weights.

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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