Your score will be calculated out of 23 points and scaled to be out of 5 points.
Part A: Explain what a probability is in your own words.
Part B: How are probabilities and odds similar?
Part C: How are probabilities and odds different?
Part D: Why does an odds-ratio of 1 indicate no association between variables?
Part E: What is the difference between empirical and theoretical probabilities?
Part F: What does it mean to say 2 events are disjoint?
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 of this data may be helpful)
Part A: Find the probability of having a stroke given someone is in the treatment group and also the probability of having a stroke given someone is in the control group.
Part B: Find the probability of someone in our data having a stroke and being in the treatment group. Are these two events disjoint?
Part C: Find the odds of having a stroke for each group.
Part D: 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 E: Is there an association between stent use and the prevalence of strokes? Use any of your answers from Parts A, C, or D to justify your answer.
Part F: Explain your findings to Part E to someone who hasn’t taken a statistics class and has a high risk of having a stroke.
The following is a description of the same Intermittent Fasting study we covered in the probabilities lab:
Time-restricted eating, a type of intermittent fasting, involves limiting the hours for eating to a specific number of hours each day, which may range from a 4- to 12-hour time window in 24 hours. Many people who follow a time-restricted eating diet follow a 16:8 eating schedule, where they eat all their foods in an 8-hour window and fast for the remaining 16 hours each day, the researchers noted. Previous research has found that time-restricted eating improves several cardiometabolic health measures, such as blood pressure, blood glucose and cholesterol levels.
In this study, researchers investigated the potential long-term health impact of following an 8-hour time-restricted eating plan. They reviewed information about dietary patterns for participants in the annual 2003-2018 National Health and Nutrition Examination Surveys (NHANES) in comparison to data about people who died in the U.S., from 2003 through December 2019.
The study included approximately 20,000 adults in the U.S. with an average age of 49 years. They found that people who followed a pattern of eating all of their food across less than 8 hours per day had a 91% higher risk of death due to cardiovascular disease.
Part A: Was this an observational study or an experiment? Explain how we know this.
Part B: Are we able to say that following the 8-hour diet caused higher probability of dying from cardiovascular disease? Explain in terms of random assignment.
Part C: What are some other reasons why those using the 8-hour intermittent fasting had higher rates of death to cardiovascular disease that may not be from the diet method itself? (Hint: Think about who is likely to use the intermittent fasting diet)