Reconsider the data from the previous exercise about investigating whether there is a relationship between undergoing surgery and whether a man dies due to prostate cancer related reasons.

a. Which of the following is the appropriate null hypothesis? Choose one.

A. Surgery recipients are equally likely as those just under observation to die of prostate cancer related reasons.

B. Surgery recipients are less likely than those just under observation to die of prostate cancer related reasons.

C. Surgery recipients are more likely than those just under observation to die of prostate cancer related reasons.

D. Surgery recipients are not equally likely as those just under observation to die of prostate cancer related reasons.

b. Which of the following is the appropriate alternative hypothesis? Choose one.

A. Surgery recipients are equally likely as those just under observation to die of prostate cancer related reasons.

B. Surgery recipients are less likely than those just under observation to die of prostate cancer related reasons.

C. Surgery recipients are more likely than those just under observation to die of prostate cancer related reasons.

D. Surgery recipients are not equally likely as those just under observation to die of prostate cancer related reasons.

Suppose that we want to use cards to perform a tactile simulation to carry out a randomization test of the appropriate hypotheses.

c. In total, how many cards will we need?

d. We need cards of different colors. How many colors do we need? How many cards of each color do we need? Explain.

e. We will shuffle the stack of cards and deal them into multiple piles. How many piles should we make and how many cards should we place in each pile? Why?

f. What statistic should we record aft er we have shuffled and dealt the cards into two piles? (Hint: Th ere is more than one correct answer here.)

g. Suppose that we have repeated the shuffle and deal many times and recorded the appropriate statistic every single time. What should we do next to fi nd the p-value?

h. Which of the following is the purpose of shuffl ing and dealing cards into two piles repeatedly and recording a chosen statistic value for each repetition?

A. To generate more samples

B. To improve accuracy of the study

C. To generate values of the statistic that could have happened by chance alone

D. All of the above