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System AlSystem B System C 18 15 16 17 17 14 16 14 Controller1 Controller 2 Controller 3 Controller 4 Controller 5 Controller 6 16 14 10 14 17 14 12 14 13

Source of Variation Sum of Squares Degrees of Freedom Mean SquareF Treatments Blocks Error Total Calculate the value of the test statistic (to 2 decimals). Calculate the critical value (to 2 decimals). Calculate the p-value (to 4 decimals). Reject null hypothesis? What is vour conclusion?

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Answer #1

applying 2 way ANOVA on above data:

Source of Variation SS df MS F
treatments 25.44 2 12.72 7.11
blocks 37.11 5 7.42
Error 17.89 10 1.79
Total 80.44 17

test statistic =7.11

critical value =4.10

p value =0.0120

reject the null hypothesis: Yes

Conclusion: conclude that there is a signifcant difference between treatment means

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