7. Dessert experiment (P. Clingan, Y. Deng, M. Geil, J. Mesaros, and J. Whitmore, 1996) The experimenters were interested in whether the melting rate of a frozen orange dessert would be affected (and, in particular, slowed down) by the addition of salt and/or sugar. At this point, they were not interested in taste testing. Six treatments were selected, as follows: 1 = 1/8 tsp salt, 1/4 cup sugar 4 = 1/4 tsp salt, 1/4 cup sugar 2 = 1/8 tsp salt, 1/2 cup sugar 5 = 1/4 tsp salt, 1/2 cup sugar 3 = 1/8 tsp salt, 3/4 cup sugar 6 = 1/4 tsp salt, 3/4 cup sugar For each observation of each treatment, the required amount of sugar and salt was added to the contents of a 12-ounce can of frozen orange juice together with 3 cups of water. The orange juice mixes were frozen in ice cube trays and allocated to random positions in a freezer. After 48 hours, the cubes were removed from the freezer, placed on half-inch mesh wire grid and allowed to melt into a container in the laboratory (which was held at 24.4 ◦C) for 30 minutes. The percentage melting (by weight) of the cubes are recorded in Table 5.20. The coded position on the table during melting is also recorded.

(a) Plot the data. Does it appear that the treatments have different effects on the melting of the frozen orange dessert?

(b) Check whether the assumptions on the one-way analysis of variance model (3.3.1) are satisfied for these data. Pay particular attention to the equal-variance assumption.

(c) Use Satterthwaite’s method to compare the pairs of treatments, using individual 99% confidence intervals. If doing the computations by hand, compute only the confidence intervals corresponding to the three most disparate pairs of treatment sample means.

(d) What conclusions can you draw about the effects of the treatments on the melting of the frozen orange dessert? If your concern was to produce frozen dessert with a long melting time, which treatment would you recommend? What other factors should be taken into account before production of such a dessert?