You roll a die 60 times and record the sample proportion of fives, and you want to test whether the die is biased to give more fives than a fair die would ordinarily give. To find the p-value for your sample data, you create a randomization distribution of proportions of fives in many simulated samples of size 60 with a fair die.

(a) State the null and alternative hypotheses.

(b) Where will the center of the distribution be? Why?

(c) Give an example of a sample proportion for which the number of 5’s obtained is less than what you would expect in a fair die.

(d) Will your answer to part (c) lie on the left or the right of the center of the randomization distribution?

(e) To find the p-value for your answer to part (c), would you look at the left, right, or both tails?

(f) For your answer in part (c), can you say anything about the size of the p-value?