This assignment is due one week after we will have our exam in class, but please be aware this material will be present on the exam and this is the best practice you will get for probability content. Finish this before the exam if you are able.
Part A (Study Design) What do we need to be true of a sample in order to generalize results to a population?
Part B (Study Design) Why does randomization of treatments to experimental units let us make causal conclusions?
Part C (Study Design) What is a sampling frame? What goes wrong if the sampling frame is missing subsets of the population?
Part D: Why does an odds-ratio of 1 indicate no association between variables?
Part E: In words, what does it mean to say 2 events are independent?
Part F: What two different ways can we use to check if 2 events are independent?
IMS - Section 2.5, Questions 3, 7, 10, 12, 15
A link to the text from which the questions come from is [here].
Open Intro Chapter 3, Questions 3.2, 3.5, 3.6, 3.8, 3.9, 3.16
Researchers recruited 451 patients with a high level of risk for strokes (when bloodflow gets cut off to the brain due to blocked blood vessels). They split these patients into two groups, a treated group that received stents (small mesh tube placed inside of vulnerable arteries) and medical management (medications, lifestyle coaching, etc.), and a control group that only received medical management. Of the 224 patients in the treatment group, 45 suffered a stroke within the first year of the study, while only 28 patients in the control group had a stroke during this time. (Hint: making a table/diagram of this data may be helpful)
Part A: Find the risk of having a stroke for someone in the treatment group and also the risk of having a stroke for someone in the control group.
Part B: Find the relative risk of having a stroke in the treatment group compared to the control group.
Part C: Interpret this relative risk value.
Part D: Find the probability of someone in our data having a stroke and being in the treatment group. Are these two events disjoint?
Part E: Find the odds of having a stroke for each group.
Part F: Find the odds ratio comparing the odds of stroke in the treatment (stent) group with the odds of a stroke in the control group.
Part G: Is there an association between stent use and the prevalence of strokes? Justify your answer using results from either Part B or Part F.
Part H: Explain your findings to Part G to someone who hasn’t taken a statistics class and has a high risk of having a stroke.