A researcher is interested in comparing the breaking strengt

A researcher is interested in comparing the breaking strength of different laminated beams made from 3 different types of glue and 3 varieties of wood. To make the comparison, 5 beams of each of the 9 combinations were manufactured and then put under a stress test. The Minitab output of a statistical analysis is give below Analysis of Variance Source DF MS F-Value P-Value 259.7 129.9 0.76 WOOD GLUE WOOD*GLUE 41274.7 2 610 1.2 17.94 0.000 318.7 0.136 170.0 36 6121.6 4413757.2 Error Total a) Calculate the value a in the above table and test the interaction hypothesis between the varieties of wood and glue effect. Use -0.01 b) Calculate the value c and test the hypothesis that the glue used does not affect the breaking strength. Use =0.01 c) Calculate the value b and test the hypothesis that the wood used does not affect the breaking strength. Use -0.01

Solution

First Question

a. To calculate the value of a is as follow;

      a= F- value of the Wood* Glue = MS/error = 318.7/170 = 1.8747

     and the corresponding calculated p- value is 0.136 which is greater than 0.01 so there is no     evedence find to reject the null hypothesis i.e there is no intraction effect between wood and Glue.

b. To calculate the value of c.

c= MS of the Glue = SS of Glue / DF of glue = 6101.2 / 2 = 3050.6

Calculated P- value of Glue is 0.000 which is less than 0.01 so we reject the null hypothesis that why , Glue used affect the breaking strength.

c. To calculate the value of b

calculated using R- software

df(0.76,2,36)

so b = 0.4557784 which is greater than 0.01 Wood used does not effect the breaking strength.

Second Question Answer

Ho : The mean time needed to mix a batch of material same for the three manufactures.

H1 : The mean time needed to mix a batch of material differ for the three manufactures.

a. Calculated P- value is 0.00029 which is less than 0.05 its mean that reject the nul hypothesis i.e. The mean time needed to mix a batch of material differ for the three manufactures.

b. Manufacture 2 having mean time need to mix a batch material significantely differ for the other two manufacture.

SUMMARY
Groups	Count	Sum	Average	Variance
Mannfactue 1	6	139	23.16666667	4.166666667
Mannfactue 2	7	188	26.85714286	5.142857143
Mannfactue 3	6	123	20.5	4.7
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	132.9148	2	66.45739348	14.14166194	0.00029	3.633723
Within Groups	75.19048	16	4.699404762
Total	208.1053	18