Three different methods for assembling a product were proposed by an industrial engineer. To investigate the number of units assembled correctly with each method, 36 employees were randomly selected and randomly assigned to the three proposed methods in such away that each method was used by 12 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 = 12,410; SSTR = 4,550.(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.)Degreesof FreedomSourceSumMeanp-valueof Variationof SquaresSquareTreatmentsErrorTotal(b) Use a = 0.05 to test for any significant difference in the means for the three assembly methods.State the null and alternative hypotheses.O H,: At least two of the population means are equal.H.: At least two of the population means are different.O Ho: H1 # Hz# HzHa: H1 = H2 = H3O Ho: H1 = H2 = H3O Ho: Not all the population means are equal.H3: H1 = Hz = H3O Ho: H, = H2 = H3H: Not all the population means are equal.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.O Do not reject Ho: There is sufficient evidence to conclude that the means of the three assembly methods are not equal.O Reject H,. There is not sufficient evidence to conclude that the means of the three assembly methods are not equal.O Reject Ho. There is sufficient evidence to conclude that the means of the three assembly methods are not equal.O Do not reject H.. There is not sufficient evidence to conclude that the means of the three assembly methods are not equal.

vay that each method was used by 12 workers. The number of units assembled correctly was recorded, and the analysis of variance procedure was applied (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 Sum Degrees of Freedom Mean p-value of Variation of Squares Square Treatments Error Total (b) Use a = 0.05 to test for any significant difference in the means for the three assembly methods. State the null and alternative hypotheses. O Hoi At least two of the population means are equal. H: At least two of the population means are different. O Hoi Hy = Hz = Hg O Ho: Not all the population means are equal. Hi Hz = Hz = Hy O Hoi Hy = Hz = Hg H: Not all the population means are equal. 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. O Do not reject H- There is sufficient evidence to conclude that the means of the three assembly methods are not equal. O Reject Hg. There is not sufficient evidence to conclude that the means of the three assembly methods are not equal. O Reject Ha. 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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Question

Three different methods for assembling a product were proposed by an industrial engineer. To investigate the number of units assembled correctly with each method, 36 employees were randomly selected and randomly assigned to the three proposed methods in such a
way that each method was used by 12 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 = 12,410; SSTR = 4,550.
(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.)
Degrees
of Freedom
Source
Sum
Mean
p-value
of Variation
of Squares
Square
Treatments
Error
Total
(b) Use a = 0.05 to test for any significant difference in the means for the three assembly methods.
State the null and alternative hypotheses.
O H,: At least two of the population means are equal.
H.: At least two of the population means are different.
O Ho: H1 # Hz# Hz
Ha: H1 = H2 = H3
O Ho: H1 = H2 = H3
O Ho: Not all the population means are equal.
H3: H1 = Hz = H3
O Ho: H, = H2 = H3
H: Not all the population means are equal.
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.
O Do not reject Ho: There is sufficient evidence to conclude that the means of the three assembly methods are not equal.
O Reject H,. There is not sufficient evidence to conclude that the means of the three assembly methods are not equal.
O Reject Ho. There is sufficient evidence to conclude that the means of the three assembly methods are not equal.
O Do not reject H.. There is not sufficient evidence to conclude that the means of the three assembly methods are not equal.

Expert Solution

Step 1

One-factor ANOVA model: In one factor ANOVA model only one factor is studied, that is only the effect on one factor is studied simultaneously. In this model there would be one dependent variable and one independent variable . The analysis of variance test is used to compare the means of more than two groups.

Assumptions for ANOVA:

Randomness and Independence: Samples are taken at random and are independent of each other.
Normality: Samples are taken from a normally distributed population.
Homogeneity of variance: The variances of probability distributions are equal.

Null hypothesis: The null hypothesis states that there is no difference in the test, which is denoted by \\[{H_0}\\] . Moreover, the sign of null hypothesis is equal \\[\\left( = \\right)\\] , greater than or equal \\[\\left( \\ge \\right)\\] and less than or equal \\[\\left( \\le \\right)\\] .

Alternative hypothesis: The hypothesis that differs from the \\[{H_\\alpha }\\] is called alternative hypothesis. This signifies that there is a significant difference in the test. The sign of alternative hypothesis is less than \\[\\left( < \\right)\\] , greater than \\[\\left( > \\right)\\] , or not equal \\[\\left( \\ne \\right)\\] .