Show all your work. Indicate clearly the methods you use, because you will be scored on the correctness of your methods as well as on the accuracy and completeness of your results and explanations.

A fair die, with its faces numbered from1

to6

, is one in which each number is equally likely to land face up when the die is rolled. On a fair die, the probability that the number6

will land face up is1

6

. A group of students wanted to investigate a claim about manipulating a fair die so that it favors one outcome. The claim states that if a fair die is put into an oven and baked at200F

for10

minutes, the inside of the die will begin to melt. When the die cools, the inside will be solid again, but with more weight toward the bottom. This shift in weight will cause the face that was up when the die cooled to land up more often that the other faces.

The students obtained a fair die and baked it according to the preceding directions. The die cooled with the number6

face up. After the die cooled, they rolled the die200

times, and the number6

landed face up43

times. Letp

represent the population proportion of times the number6

will land face up on the baked die if the die could be rolled an infinite number of times.

(a) Clarke, one of the students, constructed a95

percent confidence interval forp

as0.2150.057

. Does the interval provide convincing statistical evidence that the number6

will land face up more often on the baked die than on a fair die? Explain your reasoning.