An experiment was carried out to compare electrical resistivity for six different low-permeability concrete bridge deck mixtures. There were 26 measurements on concrete cylinders for each mixture; these were obtained 28 days after casting. The entries in the accompanying ANOVA table are based on information in an article. Fill in the remaining entries. (Round your answer for f to two decimal places.) You can use the Distribution Calculators page in SALT to find critical values and/or p-values to answer parts of this question. Source df Sum of Squares Mean Square f Mixture Error 13.989 Total 5664.505 Test appropriate hypotheses at level 0.05. State the appropriate hypotheses. (Let ?i = the true mean electrical resistivity for the ith mixture.) H0: ?1 = ?2 = ?3 = ?4 = ?5 = ?6 Ha: all six ?i's are unequal H0: ?1 = ?2 = ?3 = ?4 = ?5 = ?6 Ha: at least two ?i's are unequal H0: ?1 ≠ ?2 ≠ ?3 ≠ ?4 ≠ ?5 ≠ ?6 Ha: all six ?i's are equal H0: ?1 ≠ ?2 ≠ ?3 ≠ ?4 ≠ ?5 ≠ ?6 Ha: at least two ?i's are equal Give the test statistic. (Round your answer to two decimal places.) f = What can be said about the P-value for the test? P-value > 0.100 0.050 < P-value < 0.100 0.010 < P-value < 0.050 0.001 < P-value < 0.010 P-value < 0.001 State the conclusion in the problem context. Reject H0. There is sufficient evidence to conclude that the true mean electrical resistivity is not the same for all 6 mixtures. Reject H0. There is insufficient evidence to conclude that the true mean electrical resistivity is not the same for all 6 mixtures. Fail to reject H0. There is sufficient evidence to conclude that the true mean electrical resistivity is not the same for all 6 mixtures. Fail to reject H0. There is insufficient evidence to conclude that the true mean electrical resistivity is not the same for all 6 mixtures.

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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An experiment was carried out to compare electrical resistivity for six different low-permeability concrete bridge deck mixtures. There were 26 measurements on concrete cylinders for each mixture; these were obtained 28 days after casting. The entries in the accompanying ANOVA table are based on information in an article. Fill in the remaining entries. (Round your answer for f to two decimal places.)

You can use the Distribution Calculators page in SALT to find critical values and/or p-values to answer parts of this question.

Source	Sum of Squares	Mean Square
Mixture
Error		13.989
Total	5664.505

Test appropriate hypotheses at level 0.05. State the appropriate hypotheses. (Let ?_i = the true mean electrical resistivity for the ith mixture.)

H₀: ?₁ = ?₂ = ?₃ = ?₄ = ?₅ = ?₆
H_a: all six ?_i's are unequal H₀: ?₁ = ?₂ = ?₃ = ?₄ = ?₅ = ?₆
H_a: at least two ?_i's are unequal H₀: ?₁ ≠ ?₂ ≠ ?₃ ≠ ?₄ ≠ ?₅ ≠ ?₆
H_a: all six ?_i's are equal H₀: ?₁ ≠ ?₂ ≠ ?₃ ≠ ?₄ ≠ ?₅ ≠ ?₆
H_a: at least two ?_i's are equal

Give the test statistic. (Round your answer to two decimal places.)

f =

What can be said about the P-value for the test?

P-value > 0.100 0.050 < P-value < 0.100 0.010 < P-value < 0.050 0.001 < P-value < 0.010 P-value < 0.001

State the conclusion in the problem context.

Reject H₀. There is sufficient evidence to conclude that the true mean electrical resistivity is not the same for all 6 mixtures. Reject H₀. There is insufficient evidence to conclude that the true mean electrical resistivity is not the same for all 6 mixtures. Fail to reject H₀. There is sufficient evidence to conclude that the true mean electrical resistivity is not the same for all 6 mixtures. Fail to reject H₀. There is insufficient evidence to conclude that the true mean electrical resistivity is not the same for all 6 mixtures.

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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