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 91 100 82 100 96 89 89 95 89 88 93 80 #1) 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: A) H0: ?x ≠ ?y ≠ ?z Ha: ?x = ?y = ?z B) H0: ?x = ?y = ?z Ha: ?x ≠ ?y ≠ ?z C) H0: At least two of the population means are equal. Ha: At least two of the population means are different. D) H0: ?x = ?y = ?z Ha: Not all the population means are equal. E) H0: Not all the population means are equal. Ha: ?x = ?y = ?z #2) Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value = #3) State your conclusion. A) Reject H0. There is not sufficient evidence to conclude that the mean absorbency ratings for the three brands are not all equal. B) Do not reject H0. There is not sufficient evidence to conclude that the mean absorbency ratings for the three brands are not all equal. C)Do not reject H0. There is sufficient evidence to conclude that the mean absorbency ratings for the three brands are not all equal. D) Reject H0. There is sufficient evidence to conclude that the mean absorbency ratings for the three brands are not all equal.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.1: Measures Of Center

Problem 4GP

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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	100	82
100	96	89
89	95	89
88	93	80

#1) 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:

A) H₀: ?_x ≠ ?_y ≠ ?_z
H_a: ?_x = ?_y = ?_z

B) H₀: ?_x = ?_y = ?_z
H_a: ?_x ≠ ?_y ≠ ?_z

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

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

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

#2) Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value =

#3) State your conclusion.

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

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

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

D) Reject H₀. There is 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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