5. An experiment was performed to determine whether different types of chocolate take different amounts of time to dissolve. Forty people were divided into five groups. Each group was assigned a certain type of chocolate. Each person dissolved one piece of chocolate, and the dissolve time (in seconds) was recorded. For comparison, each person in each group also dissolved one piece of butterscotch candy; these pieces were identical for all groups. The data, which include the group, the dissolve times for both chocolate and butterscotch, the difference between the dissolve times, and the ratio of the dissolve times are presented in the following table. Note that the design is slightly unbalanced; group 3 has nine people and group 5 has only seven.

Group Chocolate Butterscotch Difference Ratio 1 135 60 75 2.25 1 865 635 230 1.36 1 122 63 59 1.94 1 110 75 35 1.47 1 71 37 34 1.92 1 81 58 23 1.40 1 2405 1105 1300 2.18 1 242 135 107 1.79 2 42 38 4 1.11 2 30 30 0 1.00 2 104 110 −6 0.95 2 124 118 6 1.05 2 75 40 35 1.88 2 80 91 −11 0.88 2 255 121 134 2.11 2 71 71 0 1.00 3 51 53 −2 0.96 3 47 40 7 1.18 3 90 155 −65 0.58 3 65 90 −25 0.72 3 27 33 −6 0.82 3 105 68 37 1.54 3 90 72 18 1.25 3 54 52 2 1.04 3 93 77 16 1.21 4 48 30 18 1.60 4 85 55 30 1.55 4 82 50 32 1.64 4 46 22 24 2.09 4 64 46 18 1.39 4 125 45 80 2.78 4 69 30 39 2.30 4 73 44 29 1.66 5 105 45 60 2.33 5 99 58 41 1.71 5 45 23 22 1.96 5 137 64 73 2.14 5 170 105 65 1.62 5 153 93 60 1.65 5 49 28 21 1.75

a. To test whether there are differences in the mean dissolve times for the different types of chocolate, someone suggests performing a one-way ANOVA, using the dissolve times for the chocolate data. Do these data appear to satisfy the assumptions for a one-way ANOVA? Explain.

b. Someone else suggests using the differences (Chocolate − Butterscotch). Do these data appear to satisfy the assumptions for a one-way ANOVA? Explain.

c. Perform a one-way analysis of variance using the ratios. Can you conclude that the mean ratio of dissolve times differs for different types of chocolate?