Two analytical methods-the AOAC method and the Babcock method-have been used to determine the amount of fat in meat. W. J. Youden in an article provided results comparing the findings of these two methods. Twenty pieces of meat were chosen at random. Each piece was subjected to both methods, and the percentage of fat estimated for it by each method was recorded. The estimates for each piece of meat, as well as the difference between the estimates for each piece of meat, are shown below. Are the two methods comparable? Is one significantly different from the other?

Piece of meat AOAC Babcock Difference 1 22.0 22.3 0.3 2 22.1 21.8 -0.3 3 22.1 22.4 0.3 4 22.2 22.5 0.3 5 24.6 24.9 0.3 6 25.3 25.6 0.3 7 25.3 25.8 0.5 8 25.6 26.2 0.6 9 25.6 26.1 0.5 10 25.9 26.7 0.8 11 26.0 26.3 0.3 12 26.2 24.9 -1.3 13 27.0 26.9 -0.1 14 27.3 28.4 1.1 15 27.7 27.1 -0.6 16 41.5 41.4 -0.1 17 41.6 41.4 -0.2 18 45.5 45.5 0.0 19 48.5 48.2 -0.3 20 49.1 47.5 -1.6 Mean 30.055 30.095 0.040 Stdev 9.304 9.008 0.652

a. What are the alternative hypothesis?

b. What are the critical value at =0.05?

c. Find the p-value for the test and interpret its value.

d. What is your conclusion at =0.02 Reject or Not Reject Null Hypothesis

e. Are the average the two methods yield the same results at =0.02?