Question

While playing a game of chance, Tarik rolled a regular six-sided die 100 times and noticed that it landed on the number 1 exactly 52 times. What could Tarik conclude about the die?

A: We are 90% confident that the true proportion of times the die would land on the number 1 is between 0.422 and 0.618. Since this includes 0.5, the die appears to be fair.

B: We are 90% confident that the true proportion of times the die would land on the number 1 is between 0.422 and 0.618. Since this is much greater than 1 out of 6, the die appears to be unfair.

C: We are 90% confident that the true proportion of times the die would land on the number 1 is between 0.438 and 0.602. Since this includes 0.5, the die appears to be fair.

D: We are 90% confident that the true proportion of times the die would land on the number 1 is between 0.438 and 0.602. Since this is much greater than 1 out of 6, the die appears to be unfair.

Answer 1

When Tarik rolled a die 100 times and observed 52 times that it landed on 1, the hypothesis test shows that the die appears to be fair as the confidence interval includes 0.5.

Step-by-step explanation:

When Tarik rolled the die 100 times and noticed that it landed on the number 1 exactly 52 times, he can conclude that the observed proportion of times the die landed on the number 1 is 52/100 = 0.52.

To determine whether the die is fair or unfair, we can use a hypothesis test.

We can perform a binomial hypothesis test with the null hypothesis that the true proportion of times the die would land on the number 1 is 1/6 (0.1667) and the alternative hypothesis that the true proportion is not 1/6.

Using the binomial proportion confidence interval, we can calculate the confidence interval for the true proportion of number 1 outcomes based on the observed proportion and the sample size.

The correct answer in this case is A: We are 90% confident that the true proportion of times the die would land on the number 1 is between 0.422 and 0.618. Since this includes 0.5, the die appears to be fair.