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, 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 = 10,790; SSTR = 4,550.

1. Set up the ANOVA table for this problem (to 2 decimals, if necessary). Round p-value to four decimal places.
   

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

   
   
2. Use = .05 to test for any significant difference in the means for the three assembly methods.
   
   The p-value is Selectless than .01between .01 and .025between .025 and .05between .05 and .10greater than .10
   
   What is your conclusion?
   SelectConclude not all means of the three assembly methods are equalCannot reject the assumption that the means of all three assembly methods are equal

Answer 1

Given:

Number of treatmnet (t) = 3

Total sample size (n) = 30 employees

10 workers each

SST = 10,790

SSTR = 4550

ANOVA TABLE:

Source of Variation	df	SS	MSS	F	P-value
Treatment	t-1 = 3-1 = 2.00	4550	=2275	9.84	0.0006
error	=n-t=30-3 = 27	=10790-4550 = 6240	231.1111111
Total	29.00	10790

df_Treatment = t-1 = 3-1 = 2

df_error = n-t = 30-3 = 27

df_total = n-1 = 30-1 = 29

SS_Error = SS_Total - SS_Treatment

SS_Error = 10790 - 4550

SS_Error = 6240

MS_Treatment = SS_Treatment - df_Treatment

MS_Treatment = 4550 / 2

MS_Treatment = 2275

MS_Error = SS_Error / df_Error

MS_Error = 6240 / 27

MS_Error = 231.111

Test statistic:

F = MS_Treatment / MS_Error

F = 2275 / 231.11

F = 9.84

b)

P-value = 0.0006

ANSWER: A

less than 0.01

P-value < , i.e. 0.0006 < 0.05, That is Reject Ho at 5% level of significance.

Conclusion:

ANSWER: A

Conclude not all means of the three assembly methods are equal