Question

A bottle cap manufacturer with four machines and six operators wants to see if variation in...

A bottle cap manufacturer with four machines and six operators wants to see if variation in production is due to the machines and/or the operators. The ANOVA table follows.

Source

Sum of Squares

df

Mean Square

Machines

125

Operators

215

Error

60

Total

400
  1. What are the degrees of freedom for the machines?
  2. What are the degrees of freedom for the operators?
  3. What are the degrees of freedom for the errors?
  4. What is the critical value of F for the machine treatment effect at the 1% level of significance?
  5. What is the mean square for machines?
  6. What is the mean square for operators?
  7. What is the mean square for error?
  8. What is the computed value of F for the machines?
  9. What is the computed value of F for the operators?
  10. Test the hypothesis that all operators are equally productive. State your decision in terms of the null hypothesis.
Math   Statistics-And-Probability   
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Answer #1
Source SS df MS
machine 125 3 41.667
operator 215 5 43.000
error 60 15 4.000
total 400 23

degrees of freedom for the machines =3

degrees of freedom for the operators =5

degrees of freedom for the errors =15

critical value of F for the machine treatment effect at the 1% level of significance =5.417

mean square for machines =41.667

mean square for operators =43

mean square for error =4

computed value of F for the machines =11.574

computed value of F for the operators =11.944

reject the null hypothesis as test statistic 11.944 is higher than critical value 4.556

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