Three different methods for assembling a product were proposed by an industrial engineer. To investigate the number of units assembled correctly with each method, 42 employees were randomiy selected and randomly assigned to the three proposed methods in such a way that each method was used by 14 workers. The number of units assembled correctly was recorded, and the analysis of variance procedure was applied to the resulting data set. The following resuts were obtained: SST - 14,150; SSTR - 4,510. (a) Set up the ANOVA table for this problem. (Round your values for MSE and Fto two decimal places, and your p-value to four decimal places.) Source of Variation Sum of Squares Degrees of Freedom Mean Pvalue Square Treatments 4610 226 0.00 Error 10000 27 37037 Total 146 10 (b) Use a- 0.05 to test for any significant difference in the means for the three assembly methods. State the null and altenative hypotheses. O Mg: Not all the population means are equal. O Mgi At least two of the population means are equal. Hại At least two of the population means are different. O Mai M" Ma s H: Not all the population means are equal. Find the value of the test statistic. (Round your answer to two decimal places.) 4.0s Find the p-value. (Round your answer to four decimal places.) Pvalue - 0.000 State your conclusion. O Do not reject Hg There is not sufficient evidence to conclude that the means of the three assembly methods are not equal. O Reject H. There is sufficient evidence to condude that the means of the three assembly methods are not equal. O Do not reject Hg. There is sufmdent 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.
Three different methods for assembling a product were proposed by an industrial engineer. To investigate the number of units assembled correctly with each method, 42 employees were randomiy selected and randomly assigned to the three proposed methods in such a way that each method was used by 14 workers. The number of units assembled correctly was recorded, and the analysis of variance procedure was applied to the resulting data set. The following resuts were obtained: SST - 14,150; SSTR - 4,510. (a) Set up the ANOVA table for this problem. (Round your values for MSE and Fto two decimal places, and your p-value to four decimal places.) Source of Variation Sum of Squares Degrees of Freedom Mean Pvalue Square Treatments 4610 226 0.00 Error 10000 27 37037 Total 146 10 (b) Use a- 0.05 to test for any significant difference in the means for the three assembly methods. State the null and altenative hypotheses. O Mg: Not all the population means are equal. O Mgi At least two of the population means are equal. Hại At least two of the population means are different. O Mai M" Ma s H: Not all the population means are equal. Find the value of the test statistic. (Round your answer to two decimal places.) 4.0s Find the p-value. (Round your answer to four decimal places.) Pvalue - 0.000 State your conclusion. O Do not reject Hg There is not sufficient evidence to conclude that the means of the three assembly methods are not equal. O Reject H. There is sufficient evidence to condude that the means of the three assembly methods are not equal. O Do not reject Hg. There is sufmdent 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.
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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Transcribed Image Text:Three different methods for assembling a product were proposed by an industrial engineer. To investigate the number of units assembled correctly with each method, 42 employees were randomily selected and randomly
assigned to the three proposed methods in such a way that each method was used by 14 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 - 14,150; SSTR - 4,510.
(a) Set up the ANOVA table for this problem. (Round your values for MSE and F to two dedimal places, and your p-value to four decimal places.)
Source
Sum
Degrees
Mean
p-value
of Variation
of Squares
of Freedom
Square
4510
2
2256
6.00
0.0056
Treatments
10000
27
37037
Error
14510
29
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 Ha: Not all the population means are equal.
O H: At least two of the population means are equal.
H: At least two of the population means are different.
O Hg: M- M2 - Hs
H: Not all the population means are equal.
H * H2 * 3
Find the value of the test statistic. (Round your answer to two decimal places.)
6.0885
Find the p-value. (Round your answer to four decimal places.)
p-value - 0.0066
State your conclusion.
O Do not reject H There is not sufficient evidence to conclude that the means of the three assembly methods are not
equal.
O Reject H. There is sufficient evidence to condude that the means of the three assembly methods are not equal.
O Do not reject H. There is sufficient evidence to conclude that the means of the three assembly methods are not equal.
O Reject Hn. There is not sufficient evidence to conclude that the means of the three assembly methods are not equal.
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