Question:

1.The following is paraphrased from a Web site that discusses the sensitivity and specificity of the PSA (Prostate Specific Antigen) test for prostate cancer. In a larger study (243 subjects), Ward and colleagues used a cutoff ratio of 0.15 to demonstrate 78% sensitivity and 69% specificity in the diagnosis of prostate cancer. In contrast, tPSA measurements alone yielded equivalent sensitivity but only 33% specificity. These reports are encouraging, but larger clinical studies are required for determination of the optimal fPSA:tPSA cutoff ratio.

What does the figure 69% specificity in the above study mean?

A patient who does not have the antigen has a 69% chance that the test reads negative.

A patient who has the antigen has a 69% chance that the test reads negative.

A patient who has the antigen has a 69% chance that the test reads positive.

A patient who does not have the antigen has a 69% chance that the test reads positive.

2.The following is paraphrased from a Web site that discusses the sensitivity and specificity of the PSA (Prostate Specific Antigen) test for prostate cancer. In a larger study (243 subjects), Ward and colleagues used a cutoff ratio of 0.15 to demonstrate 78% sensitivity and 69% specificity in the diagnosis of prostate cancer. In contrast, tPSA measurements alone yielded equivalent sensitivity but only 33% specificity. These reports are encouraging, but larger clinical studies are required for determination of the optimal fPSA:tPSA cutoff ratio.

What does the figure 69% specificity in the above study mean?

A patient who has the antigen has a 69% chance that the test reads negative.

A patient who has the antigen has a 69% chance that the test reads positive.

A patient who does not have the antigen has a 69% chance that the test reads negative.

A patient who does not have the antigen has a 69% chance that the test reads positive.

3.Your wife has asked you to pick up a bottle of her favorite shampoo. When you get to the store, you can't remember which brand she uses. There are nine shampoo brands on the shelf. If you select one, what is the probability that you get the right brand of shampoo? Leave your answer as a fraction.

Of the nine bottles, four are blue, three are white, and two are red. You remember that your wife's shampoo comes in awhitebottle. What is the probability that you get the right bottle with this additional information? Leave your answer as a fraction.

Problem 1: A Central Limit Theorem Simulation Here we will perform a Central Limit Theorem simulation similar to the ones done in class. That is: . Pick a distribution (that was not presented in class) . Justify that the distribution will abide by the central limit theorem . Find a parameter set and value for / where we can see that the central limit theorem clearly applies . Find a parameter set and value for / where we can see that the central limit theorem does not apply . Code must be submitted (preferably in R, but MATLAB, Python, ForTran, and C++ will also be accepted).M4A1 Discussion Forum: Central Limit Theorem Discussion Board Topics: 1. Explain the central limit theorem. 2. Why is the central limit theorem an important concept in statistics? Discussion Board Guidelines: You will need to respond to a peer's posting, and evidence of critical thinking is required