In a completely randomized experimental design, three brands of paper towels were tested for their ability to absorb water. Equal-size towels were used, with four sections of towels tested per brand. The absorbency rating data follow. Brand x y z 91 99 84 101 95 87 87 95 88 89 103 73 At a 0.05 level of significance, does there appear to be a difference in the ability of the brands to absorb water? State the null and alternative hypotheses. -H0: Not all the population means are equal. Ha: ?x = ?y = ?z -H0: ?x ≠ ?y ≠ ?z Ha: ?x = ?y = ?z --H0: ?x = ?y = ?z Ha: Not all the population means are equal. -H0: At least two of the population means are equal. Ha: At least two of the population means are different. -H0: ?x = ?y = ?z Ha: ?x ≠ ?y ≠ ?z Find the value of the test statistic. (Round your answer to two decimal places.) Statistic=?? Find the p-value. (Round your answer to three decimal places.) p-value = ?? State your conclusion. -Do not reject H0. There is sufficient evidence to conclude that the mean absorbency ratings for the three brands are not all equal. -Reject H0. There is sufficient evidence to conclude that the mean absorbency ratings for the three brands are not all equal. -Reject H0. There is not sufficient evidence to conclude that the mean absorbency ratings for the three brands are not all equal. -Do not reject H0. There is not sufficient evidence to conclude that the mean absorbency ratings for the three brands are not all equal.

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

In a completely randomized experimental design, three brands of paper towels were tested for their ability to absorb water. Equal-size towels were used, with four sections of towels tested per brand. The absorbency rating data follow.

Brand
x	y	z
91	99	84
101	95	87
87	95	88
89	103	73

At a 0.05 level of significance, does there appear to be a difference in the ability of the brands to absorb water?

State the null and alternative hypotheses.

-H₀: Not all the population means are equal.
H_a: ?_x = ?_y = ?_z

-H₀: ?_x ≠ ?_y ≠ ?_z
H_a: ?_x = ?_y = ?_z

--H₀: ?_x = ?_y = ?_z
H_a: Not all the population means are equal.

-H₀: At least two of the population means are equal.
H_a: At least two of the population means are different.

-H₀: ?_x = ?_y = ?_z
H_a: ?_x ≠ ?_y ≠ ?_z

Find the value of the test statistic. (Round your answer to two decimal places.)

Statistic=??

Find the p-value. (Round your answer to three decimal places.)

p-value = ??

State your conclusion.

-Do not reject H₀. There is sufficient evidence to conclude that the mean absorbency ratings for the three brands are not all equal.

-Reject H₀. There is sufficient evidence to conclude that the mean absorbency ratings for the three brands are not all equal.

-Reject H₀. There is not sufficient evidence to conclude that the mean absorbency ratings for the three brands are not all equal.

-Do not reject H₀. There is not sufficient evidence to conclude that the mean absorbency ratings for the three brands are not all equal.

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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