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.

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 vaccine 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 male and vaccinated 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 male or vaccinated develops Covid-19? To earn full credit, write your answer using probability notation, as a fraction and decimal rounded to three decimal places.

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 vaccine 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 male and vaccinated 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 male or vaccinated 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 Q10 A study was conducted to investigate how effective a new diet was in lowering cholesterol.  Ten subjects’ cholesterol is measured before and after they eat meals from a new diet developed by the researchers. Cholesterol is recorded in units milligrams per deciliter of blood (mg/dL), with a larger number corresponding to higher cholesterol. Assume the population of differences is normally distributed.  Subject A B C D E F G H I J Before 239 240 230 242 231 220 240 237 227 249 After 230 230 231 239 220 220 235 230 223 240 Difference (before minus after)   Explain why this data is paired.  Calculate and interpret a 99% confidence interval for the mean difference in cholesterol before and after utilizing the new diet. Show all steps of building a confidence interval and round all calculated values to two decimal places. Write desmos functions used to compute sample statistics.  Sandra calculated a 90% confidence interval for the mean difference in cholesterol before and after utilizing the new diet to be (3.28, 8.12). What can you reasonably conclude about the new diet based on the interval?

Exam Question 10 Let  represent the Covid vaccination rate in Rancho Cucamonga. The null and alternative hypotheses are , . Given this information, write the claim being tested. Sandy tests the claim and finds the P-value to be 0.03. Write the conclusion in plain language if the level of significance is 5%.

Exam Question 4 Below is a clickable desmos graph of stacked boxplots displaying the distribution of salaries of people who have earned a doctorate and the distribution of salaries of people whose highest degree earned is a bachelor’s degree. Compare and contrast the typical annual salary of the two groups. Speak specifically about the center of each distribution in your explanation.  Compare and contrast the variability in annual salary of the two groups. Speak specifically about the spread of each distribution in your explanation. (Hint: there are two measures of spread that you should include in your answer). Identify the shape of each distribution.

Prof Rea’s Exam Q10 The given scatterplot was generated from data for the first two decades of flu reporting.   The LSR line has equation