Yogurt research. An experiment to determine the effect of several methods of preparing cultures for use in commercial yogurt was conducted by a food science research group. Three batches of yogurt were prepared using each of three methods: traditional, ultrafiltration, and reverse osmosis. A trained expert then tasted each of the 9 samples, presented in random order, and judged them on a scale from 1 to 10.

A partially complete Analysis of Variance table of the data follows.

Sum of Degrees of Mean Source Squares Freedom Square F-ratio Treatment 17.300 Residual 0.460 Total 17.769

a) Calculate the mean square of the treatments and the mean square of the error.

b) Form the F-statistic by dividing the two mean squares.

c) The P-value of this F-statistic turns out to be 0.000017.

What does this say about the null hypothesis of equal means?

d) What assumptions have you made in order to answer part c?

e) What would you like to see in order to justify the conclusions of the F-test?

f) What is the average size of the error standard deviation in the judge’s assessment?