Prof Rea’s Exam Q3 A researcher conducted a study to determine if an antidepressant reduces the chance of migraines. He randomly assigned 300 patients to take the antidepressant every day and 300 patients to take a placebo every day. After a certain length of time, he reported the number of migraine days in the patients who took the antidepressant every day and in those who did not take the antidepressant every day. Identify the explanatory and response variables.

Exam Question 6 A student completes the following question incorrectly. Explain the mistake they made, and fix the mistake:  Question: Consider the following two distributions:  The time doctoral students spend studying for their midterm exam. The time high school students spend studying for their midterm exam.  Which of these distributions would have a larger standard deviation? Explain your answer. Answer: I believe that time doctoral students spend studying for a midterm exam has a higher standard deviation because their midterm will be harder, and therefore they will study longer than high school students.

Exam Question 7 The following table shows the number of people who developed Covid-19 in a sample of 94 total participants who developed Covid-19. Participants are organized by their reported gender and whether they received a vaccine or placebo in the trial.  Vaccine Placebo Total Male 4 42 46 Female 3 36 39 Other 1 8 9 Total 8 86 94 What is the probability of someone with a placebo developing Covid-19? To earn full credit, write your answer using probability notation, as a fraction and decimal rounded to three decimal places.  What is the probability that someone who is female and takes a placebo develops Covid-19? To earn full credit, write your answer using probability notation, as a fraction and decimal rounded to three decimal places. Given a subject is female, what is the probability that someone who takes a placebo develops Covid-19? To earn full credit, write your answer using probability notation, as a fraction and decimal rounded to three decimal places. A student answers the following question incorrectly. Explain the mistake they made and answer the question correctly (use proper notation and justify your answer with a calculation).  Question: Is it more likely to meet a man with a placebo that developed Covid-19 or a woman with a placebo that develops Covid-19? Answer: Since there are more men who received the placebo than women, you are more likely to meet a man with a placebo that developed Covid-19. What is the probability that someone who is female or takes a placebo develops Covid-19? To earn full credit, write your answer using probability notation, as a fraction and decimal rounded to three decimal places.

Prof Rea’s Exam Q6 A statistician wanted to examine the proportions of various racial groups that are incarcerated in California. She collects data from a random sample of 256 Californian’s that have been arrested and charged with a crime. The following table shows this sample organized into the categories of race, and whether they are incarcerated or not.  White Black Other Total Incarcerated 12 54 27 159 Not Incarcerated 64 34 65 97 Total 76 88 92 256 Calculate the probability that a randomly selected individual from the sample is white. Use probability notation and write your answer as a fraction and decimal rounded to three decimal places. Calculate the probability that a randomly selected individual from the sample is white and incarcerated. Use probability notation and write your answer as a fraction and decimal rounded to three decimal places. Are white individuals, black individuals, or individuals with other race more likely to be incarcerated? Explain and show each calculation with proper probability notation to earn full credit. 

Prof Rea’s Exam Q7 Given below is a clickable scatterplot generated from data taken from 11 high school students. What is the direction of the relationship?     

Prof Rea’s Exam Q6 Given below is a clickable scatterplot generated from data taken from 24 parents. What is the strength of the relationship? Explain why you think this.   

Exam Question 5 The two given distributions have the same mean. Without doing any calculations, identify which distribution has less variability. Explain why you think this.  a.  b.  

Exam Question 5 The two given distributions have the same mean. Without doing any calculations, identify which distribution has less variability. Explain why you think this.  a.  b.  

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Prof Rea’s Exam Q2 A researcher conducted a study to determine if an antidepressant reduces the chance of migraines. He randomly assigned 300 patients to take the antidepressant every day and 300 patients to take a placebo every day. After a certain length of time, he reported the number of migraine days in the patients who took the antidepressant every day and in those who did not take the antidepressant every day. What is the most important reason for the researcher to randomly assign patients to one of the two groups? So that equal amounts of antidepressants and placebo would be used during the experiment. So that the results of the study will generalize. So that the groups are similar, or have no real difference, prior to the treatment. So that there are an equal number of people in both groups.