A fair die with its faces numbered from 1 to 6 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 number 6 will land face up is 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 at 200 F for 10 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 number 6 face up After the die cooled they rolled the die 200 times and the number 6 landed face up 43 times Let p represent the population proportion of times the number 6 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 a 95 percent confidence interval for p as 0 215 0 057 Does the interval provide convincing statistical evidence that the number 6 will land face up more often on the baked die than on a fair die Explain your reasoning BIU X X C2E E BI U X X 3 C 2 a b Aurelia another student suggested they conduct a significance test to investigate the claim She tested the hypotheses Ho p versus H p at the significance level of a 0 05 She obtained a test statistic of 1 83 with a p value of 0 033 Do the results of the significance test agree with the results of Clarke s confidence interval in part a Explain your reasoning O E Pa 0 10000 Word Limit