Three different methods for assembling a product were proposed by an industrial engineer. To investigate the number of units assembled correctly with each method, 30 employees were randomly selected and randomly assigned to the three proposed methods in such a way that each method was used by 10 workers. The number of units assembled correctly was recorded, and the analysis of variance procedure was applied to the resulting data set. The following results were obtained: SST = 10,800; SSTR = 4,520. (a) Set up the ANOVA table for this problem. (Round your values for MSE and F to two decimal places, and your p-value to four decimal places.) Source of Variation Sum of Squares Degrees of Freedom Mean Square F p-value Treatments Error Total (b) Use ? = 0.05 to test for any significant difference in the means for the three assembly methods. State the null and alternative hypotheses. H0: Not all the population means are equal. Ha: ?1 = ?2 = ?3H0: ?1 ≠ ?2 ≠ ?3 Ha: ?1 = ?2 = ?3 H0: ?1 = ?2 = ?3 Ha: Not all the population means are equal.H0: ?1 = ?2 = ?3 Ha: ?1 ≠ ?2 ≠ ?3H0: At least two of the population means are equal. Ha: At least two of the population means are different. Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. Reject H0. There is not sufficient evidence to conclude that the means of the three assembly methods are not equal.Do not reject H0. There is not sufficient evidence to conclude that the means of the three assembly methods are not equal. Do not reject H0. There is sufficient evidence to conclude that the means of the three assembly methods are not equal.Reject H0. There is sufficient evidence to conclude that the means of the three assembly methods are not 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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Three different methods for assembling a product were proposed by an industrial engineer. To investigate the number of units assembled correctly with each method, 30 employees were randomly selected and randomly assigned to the three proposed methods in such a way that each method was used by 10 workers. The number of units assembled correctly was recorded, and the analysis of variance procedure was applied to the resulting data set. The following results were obtained: SST = 10,800; SSTR = 4,520.

(a)

Set up the ANOVA table for this problem. (Round your values for MSE and F to two decimal places, and your p-value to four decimal places.)

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F	p-value
Treatments
Error
Total

(b)

Use ? = 0.05 to test for any significant difference in the means for the three assembly methods.

State the null and alternative hypotheses.

H₀: Not all the population means are equal.
H_a: ?₁ = ?₂ = ?₃H₀: ?₁ ≠ ?₂ ≠ ?₃
H_a: ?₁ = ?₂ = ?₃ H₀: ?₁ = ?₂ = ?₃
H_a: Not all the population means are equal.H₀: ?₁ = ?₂ = ?₃
H_a: ?₁ ≠ ?₂ ≠ ?₃H₀: At least two of the population means are equal.
H_a: At least two of the population means are different.

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

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

p-value =

State your conclusion.

Reject H₀. There is not sufficient evidence to conclude that the means of the three assembly methods are not equal.Do not reject H₀. There is not sufficient evidence to conclude that the means of the three assembly methods are not equal. Do not reject H₀. There is sufficient evidence to conclude that the means of the three assembly methods are not equal.Reject H₀. There is sufficient evidence to conclude that the means of the three assembly methods are not 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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