Jaimie Kwon Page 4 10/13/2004
Stat {4601, 6872} Quiz #1 (50 minutes)
• Open book and open note.
• Use a simple calculator if necessary.
• Show your work. (E.g. Next to each numerical answer, you need to put things like
P0.01(B≥3) or something equivalent)
• Grad students need to do problems with * as well. Undergrad will get extra credit by
solving them.
#1. (7 points)
For patients suffering from arthritis, a traditional pain relief treatment exists but has a side
effect of problems in the kidney and resulting in 5% risk of heart attacks and strokes after 3
months of treatment. A new medical treatment is proposed that reduces the chances of the
kidney problem. But a question has been raised that the new drug may increase the risk of
heart attacks and strokes. To test this, a clinical trial data has been collected for 10 patients
and it turned out that 1 of them had the problem.
1) What assumptions does one need to check before applying the binomial test? Use the plain
language and terms of the subject field that is understandable to general audience. (1 pt)
2) Formulate the null and alternative hypotheses. (1 pt)
3) Give a general definition of the p-value. Then compute the p-value for the above data. (1 pt)
4) What is the significance level of a test that rejects the null hypothesis when the number
of patients experiencing a heart attack is greater than or equal to 3? (1 pt)
5) What is the power of the test in 4) at the alternative ‘the true chance of a patient having a
heart attack or stroke is 10%’? What is the probability of Type II error in such case? (1 pt)
