6. Three different machines are being considered for use in manufacturing rubber

Question

6. Three different machines are being considered for use in manufacturing rubber seals. The machines are being compared with respect to tensile strength of the product. A random sample of 4 seals from each machine is used to determine whether the mean tensile strength varies from machine to machine. Perform an ANOVA test to determine whether the tensile strengths are equivalent for the three machines. Use alpha = .05. The following are tensile strength measurements in kilograms per square centimeter:

a.) State Ho and Ha

b.) calculate SST, SSE, and MST

c.) calculate F-calculated and F-critical, what is the decision(reject or accept Ho)?

Please show work! I know how to just put this into excel to give me the data I need, I'm struggling with the calculations of SST, MST, SSE , F-calculated and F-critical

Machine samples M1 M2 M3 17.5 16.4 20.3 16.9 19.2 15.7 15.8 17.7 17.8 18.6 15.4 18.9 Sample mean 17.20 17.18 18.18 Sample standard deviation 1.17 1.65 1.94 Grand mean 17.52

Explanation / Answer

a) H0: There is no difference between means of three groups

H1: There is a difference between means of three groups.

b) From Excel

SST=2.602

SSE=23.535

MST=1.3008

c) F cal=0.4974

F critial value=4.2565

F cal < F critical value, we donot reject the H0.

Hence claim is not significant.

Anova: Single Factor SUMMARY Groups Count Sum Average Variance M1 4 68.8 17.2 1.366667 M2 4 68.7 17.175 2.709167 M3 4 72.7 18.175 3.769167 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 2.601667 2 1.300833 0.497451 0.623861 4.256495 Within Groups 23.535 9 2.615 Total 26.13667 11

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