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.
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
Ha: ?x = ?y = ?z
Ha: ?x = ?y = ?z
B) H0: ?x = ?y = ?z
Ha: ?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.
Ha: At least two of the population means are different.
D) H0: ?x = ?y = ?z
Ha: Not all the population means are equal.
Ha: Not all the population means are equal.
E) H0: Not all the population means are equal.
Ha: ?x = ?y = ?z
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.
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