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 16. 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.
(c) Two standard normal curves are shown below, one for the confidence interval calculated in part (a) and one for the significance test conducted in part (b).
(i) For the confidence interval curve, label the critical values for the 95% confidence level and shade the area that represents values in the outer 5%.
(ii) For the significance test curve, label the critical value for the 5% significance level and shade the area representing the values of z that would lead to a rejection of the null hypothesis in part (b).
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