Question

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.

Answer 1

The confidence interval constructed provides statistical evidence that the number 6 lands face up more often than it would on a fair die, as the interval is entirely above the expected fair proportion of 1/6.

Step-by-step explanation:

Clarke constructed a 95 percent confidence interval for 'p' as 0.215±0.057. This interval suggests that the true proportion 'p' of times number 6 will land face up is estimated to be between 0.158 (0.215-0.057) and 0.272 (0.215+0.057). On a fair die, the probability of a certain number appearing is 1/6, which is approximately 0.1667. Because the entire confidence interval is above 0.1667, it does provide statistical evidence that number 6 is landing face up more often than it would on a fair die. However, whether the evidence is 'convincing' depends on the context and the stakes of the claim in question. If this was a baked die, meaning it has been modified to change the probability, then this would likely be considered convincing evidence.

Answer 2

Step-by-step explanation:

With a fair die, the probability of rolling a 6 is 1/6 or 0.167.

For the baked die, the low end of the confidence interval is 0.215 − 0.057 = 0.158.

Since 0.167 is within the range of the confidence interval, there is not convincing statistical evidence that a baked die will have a higher probability of rolling a 6 than a fair die.