Question

5.2.5
​Researchers Wilt et al. (New England Journal of Medicine, 2012) investigated whether surgery, compared to just observation, was (more) effective in improving men’s survival chances after being diagnosed with prostate cancer. The researchers identified 731 men with localized prostate cancer who volunteered to participate. They randomly assigned 364 men to surgery and the remaining 367 to observation. All participants were followed for about 10 years. In those 10 years, 21 surgery recipients died of prostate cancer related reasons compared to 31 observation recipients.
Investigate whether there is a relationship between undergoing surgery and whether a man dies due to prostate cancer related reasons.

  
Which of the following is the appropriate null hypothesis?

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

  
Which of the following is the appropriate alternative hypothesis?

A: Surgery recipients are more likely than 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 equally likely as 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. In total, how many cards will we need?

A: 731

B: 367

C: 364

D: 52

  

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

A: Two Colors 52 of one color and 679 of the other?

B: Three Colors: 600 of one color, 52 of the second color, and 79 of the third color?

C: Two Colors: 364 of one color and 367 of the other color?

D: Three Colors: 364 of one color, 51 of the second color, and 315 of the third color?

  
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?

A: Two Colors: 364 of one color and 367 of the other?

B: Two Piles: 364 in one pile and 367 in the other pile?

C: Three Colors: 364 of one color, 52 of the second color, and 315 of the third color?

D: Three Piles: 301 in one pile, 290 in the second pile, and?

What statistic should we record after we have shuffled and dealt the cards into two piles?

A: Difference in number of cards in two piles

B: Difference in proportions or relative risk

C: Number of cards in a pile

D: Mean number of cards

  
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 find the p-value?

A: Find how often the observed statistic or greater occurred in the simulations (one tail).

B: Find how often the simulation results in the observed value or a more extreme value (both tails).

C: Find how often the difference in proportions is the same as in the simulations (one tail).

D: Find how often the difference in proportions is the same as in the simulations (both tails).

Answer 1

(A) Null hypothesis:

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

OPTION (D) is correct answer .

(B) Alternative hypothesis :

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

OPTION (D) is correct answer .

(C)  In total, how many cards will we need:

we need total cards are 731

OPTION (A ) is correct answer .

(D) How many colors do we need:

we needed colors are

Two Colors: 364 of one color and 367 of the other color.

OPTION (C) is correct answer

(E) how many cards should we place in each pile:

we needed to each pile is

  Two Piles: 364 in one pile and 367 in the other pile.

OPTION (B) is correct answer

(F)

What statistic should we record after we have shuffled and dealt the cards into two piles:

The statistic is  Difference in proportions or relative risk.

OPTION (B) is correct answer

(G) What should we do next to find the p-value:

p-value , find how often the difference in proportions is the same as in the simulations (both tails).

OPTION (D) is correct answer .