Please complete the table above. To determine the effect of several methods of p

Question

Please complete the table above.

To determine the effect of several methods of preparing cultures for use in commercial yogurt, three batches of yogurt were prepared using each of the three methods A trained expert then tasted each of the 9 samples, presented in random order, and judged them on a scale of 1 to 10. A partially complete analysis of variance table of the data follows. Complete parts a through f Source Treatment Residual Total F-ratio Sum of Squares 22.282 0.387 22.669 Degrees of Freedom Mean Square

Explanation / Answer

The completed table with the calculation is given below.

Degree of freedom for treatment = Number of methods (treatment) - 1 = 3 - 1 = 2

Degree of freedom for residual = Number of observations - Number of methods (treatment) = 9 - 3 = 6

Degree of freedom for total = Number of observations - 1 = 9 - 1 = 8

Mean square for treatment = Sum of squares for treatment / Degree of freedom for treatment

= 22.282 / 2 = 11.141

Mean square for residual = Sum of squares for residual / Degree of freedom for residual

= 0.387 / 6 = 0.0645

Mean square for total = Sum of squares for total / Degree of freedom for total

= 22.669 / 8 = 2.8336

F-ratio = Mean square for treatment / Mean square for residual

= 11.141 / 0.0645 = 172.7287

Source Sum of Squares Degrees of Freedom Mean Square F-ratio Treatment 22.282 2 11.141 172.7287 Residual 0.387 6 0.0645 Total 22.669 8 2.8336

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