Three different assembly methods have been proposed for a new product. A completely randomized experimental design was chosen to determine which assembly method results in the greatest number of parts produced per hour, and 30 workers were randomly selected and assigned to use one of the proposed methods. The number of units produced by each worker follows. Method A B C 96 92 99 72 99 94 94 92 88 99 56 66 74 78 60 90 92 76 100 85 85 87 72 72 91 91 88 107 83 72 #1) Use these data and test to see whether the mean number of parts produced is the same with each method. Use ? = 0.05. State the null and alternative hypotheses: A) H0: Not all the population means are equal. Ha: ?A = ?B = ?C B) H0: ?A = ?B = ?C Ha: ?A ≠ ?B ≠ ?C C) H0: At least two of the population means are equal. Ha: At least two of the population means are different. D) H0: ?A = ?B = ?C Ha: Not all the population means are equal. E) H0: ?A ≠ ?B ≠ ?C Ha: ?A = ?B = ?C #2) Find the value of the test statistic (Round answer to two decimal places), and the P value (round to three decimal places). #3) State your conclusion: A) Do not reject H0. There is not sufficient evidence to conclude that the mean number of parts produced is not the same with each method. B) Do not reject H0. There is sufficient evidence to conclude that the mean number of parts produced is not the same with each method. C) Reject H0. There is not sufficient evidence to conclude that the mean number of parts produced is not the same with each method. D) Reject H0. There is sufficient evidence to conclude that the mean number of parts produced is not the same with each method.

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Description: Three different assembly methods have been proposed for a new product. A completely randomized experimental design was chosen to determine which assembly method results in the greatest number of parts produced per hour, and 30 workers were randomly s

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 assembly methods have been proposed for a new product. A completely randomized experimental design was chosen to determine which assembly method results in the greatest number of parts produced per hour, and 30 workers were randomly selected and assigned to use one of the proposed methods. The number of units produced by each worker follows.

Method
A	B	C
96	92	99
72	99	94
94	92	88
99	56	66
74	78	60
90	92	76
100	85	85
87	72	72
91	91	88
107	83	72

#1) Use these data and test to see whether the mean number of parts produced is the same with each method. Use ? = 0.05.

State the null and alternative hypotheses:

A) H₀: Not all the population means are equal.
H_a: ?_A = ?_B = ?_C

B) H₀: ?_A = ?_B = ?_C
H_a: ?_A ≠ ?_B ≠ ?_C

C) H₀: At least two of the population means are equal.
H_a: At least two of the population means are different.

D) H₀: ?_A = ?_B = ?_C
H_a: Not all the population means are equal.

E) H₀: ?_A ≠ ?_B ≠ ?_C
H_a: ?_A = ?_B = ?_C

_{#2) Find the value of the test statistic (Round answer to two decimal places), and the P value (round to three decimal places).}

_{#3) State your conclusion:}

_{A) Do not reject H0. There is not sufficient evidence to conclude that the mean number of parts produced is not the same with each method.}

_{B) Do not reject H0. There is sufficient evidence to conclude that the mean number of parts produced is not the same with each method.}

_{C) Reject H0. There is not sufficient evidence to conclude that the mean number of parts produced is not the same with each method.}

_{D) Reject H0. There is sufficient evidence to conclude that the mean number of parts produced is not the same with each method.}

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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Method
A	B	C
96	92	99
72	99	94
94	92	88
99	56	66
74	78	60
90	92	76
100	85	85
87	72	72
91	91	88
107	83	72

Method
A	B	C
96	92	99
72	99	94
94	92	88
99	56	66
74	78	60
90	92	76
100	85	85
87	72	72
91	91	88
107	83	72

Method
A	B	C
96	92	99
72	99	94
94	92	88
99	56	66
74	78	60
90	92	76
100	85	85
87	72	72
91	91	88
107	83	72