PLEASE INCLUDE A SUMMARY EXPLAINING AND DETAILING ALL THE DECISIONS! Tensile pro

Question

PLEASE INCLUDE A SUMMARY EXPLAINING AND DETAILING ALL THE DECISIONS!

Tensile properties of 3 different adhesive batches are being evaluated. The investigator wants to determine if one of the batches differs significantly from the other batches. a) State the null and alternate hypothesis. b) What is the decision rule? c) Compute SST, SSE and SS total. d) After running the ANOVA table, explain whether there is a difference between adhesives and WHY you decided this. e) What is the degree of freedom for the treatments, error and total? f) If H_0 is rejected, can we conclude that adhesive 1 and adhesive 2 are different? Use the 95% level of confidence. g) What about Adhesive 2 and Adhesive 3? Are they different? Follow f.

Explanation / Answer

SOlA:

Null hypothesis:

Ho:All means are equal

mean(adhesive1)=mean(adhesive2)=mean(adhesive3)

Alternative hypothesis:

H1:alleast one of the means are different

Level of significance=0.05

Solutionb:

if p<0.05 reject null hypothesis

if p>0.05 accept null hypothesis

Solutionc:

SS treatment-129.678

SSE----62.689

SS total---192.367

SOlutiond:

F statistic calculated=27.926

p value=2.67*10^-7<0.05

Reject Null hypothesis

There is difference between adhesives

Solutione:

degrees of freedom for error=2

degrees of freedomffor treatment=27

degrees of freedom for total=29

Anova: Single Factor SUMMARY Groups Count Sum Average Variance adhesive1 10 61.2 6.12 4.221778 adhesive2 10 21.9 2.19 0.038778 adhesive3 10 69.6 6.96 2.704889 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 129.678 2 64.839 27.926 2.67E-07 3.354131 Within Groups 62.689 27 2.321815 Total 192.367 29

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