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.

Continue to the next page...

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 ˆ’ 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?

Transcribed Image Text:

IO-564720891055881 呂呂22 1578 pen 75 30 59 35 34 23 300-40-66 35 1 3027 65 25-6 co o 53578558008 0111305 3673503331149275 45 6 ola-35 65 22 110 71 42 42 30 04 24 75 80 55 71 51 47 90 65 27 1811 0 1 1 1 1 1 1 2 2 2 2 2 2 2 2 3 3 3 3 3 1054998063164255 t-520. 2 6 5 6 0 3 7 3 6 3 7 9 1 667 221211211 1 7826802480990123501 3 1 1 1 1 3 3 2 1 8 326427662 38 67573552 4 4 3 4 4 5 2 6 0 9 2 la 5 3 5 2 4 5 5 0 935957039 9 5 4 4 6 7 9 4 3 7 5 4 0959 4 8 8 4 62670 9 4 3754 0|3333444444445555555