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,  employees were randomly selected and randomly assigned to the three proposed methods in such a way that each method was used by  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: ; .

a. Set up the ANOVA table for this problem (to 2 decimals, if necessary).

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F	p-value (to 4 decimals)
Treatments
Error
Total

b.Use  to test for any significant difference in the means for the three assembly methods.

Calculate the value of the test statistic (to 2 decimals).

The -value is - Select your answer -less than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 12

What is your conclusion?

- Select your answer -Conclude not all means of the three assembly methods are equalCannot reject the assumption that the means of all three assembly methods are equalItem 13

Answer 1

(A)

SOURCE OF VARIATION	SUM OF SQUARE	DEGREES OF FREEDOM	MEAN SQUARE	F	P-VALUE
TREATMENTS	4560	2	2280	9.87	0.0006
ERROR	6240	27	231.11
TOTAL	10800	29

(b)

using F table (2 degrees of freedom numerator and 27 denominators), p-value is less than 0.01.

•Using Excel, the P-value corresponding to f = 9.87 is 0.0006.

•Becausep-value< α= 0.05, we reject the null hypothesis that the means of the three assembly methods are equal.

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