12. Balloon experiment Prior to 1985, the experimenter (Meily Lin) had observed that some colors of birthday balloons seem to be harder to inflate than others. She ran this experiment to determine whether balloons of different colors are similar in terms of the time taken for inflation to a diameter of 7 inches. Four colors were selected from a single manufacturer. An assistant blew up the balloons and the experimenter recorded the times (to the nearest 1/10 second) with a stop watch. The data, in the order collected, are given in Table 3.13, where the codes 1, 2, 3, 4 denote the colors pink, yellow, orange, blue, respectively.

(a) Plot inflation time versus color and comment on the results.

(b) Estimate the mean inflation time for each balloon color, and add these estimates to the plot from part (a).

(c) Construct an analysis of variance table and test the hypothesis that color has no effect on inflation time.

(d) Plot the data for each color in the order that it was collected. Are you concerned that the assumptions on the model are not satisfied? If so, why? If not, why not?

(e) Is the analysis conducted in part

(c) satisfactory?