Engage NY Eureka Math Algebra 2 Module 4 Lesson 30 Answer Key
Eureka Math Algebra 2 Module 4 Lesson 30 Exercise Answer Key
Exercises 1 – 7:
Pericarditis is an inflammation (irritation and swelling) of the pericardium, the thin sac that surrounds the heart. When extra fluid builds up between the two layers of the pericardium, the heart’s actions are restricted. An experiment reported in the article “A Randomized Trial of Colchicine for Acute Pericarditis” in The New England Journal of Medicine (October 2013) tested the effects of the drug colchicine on acute pericarditis.
Read the abstract of the article, and answer the following questions:
How many treatment groups are there?
There are 2 treatment groups.
What treatments are being compared?
The two treatment groups are colchicine and placebo with the standard anti-inflammatory treatment.
Is there a placebo group? Explain.
Yes, the second treatment group is a placebo in addition to an aspirin or an ibuprofen.
How many subjects are in each treatment group?
There are 120 subjects in each treatment group.
Do you think that the number of subjects in each treatment group is enough? Explain.
Yes; 120 subjects should be large enough to allow the researchers to see the variation in treatment effects.
What method was used to assign the subjects to the treatment groups? Explain why this is important.
The subjects were randomly assigned to the treatment groups. This is important because the random assignment evenly disperses the extraneous variables into both treatment groups.
Suppose newspaper reporters brainstormed some headlines for an article on this experiment. These are their suggested headlines:
A. “New Treatment Helps Pericarditis Patients”
B. “Colchicine Tends to Improve Treatment for Pericarditis”
C. “Pericarditis Patients May Get Help”
Which of the headlines above would be best to use for the article? Explain why.
Headline A would be the best because this is a well-designed experiment. Therefore, a cause-and-effect relationship has been established. Headlines B and C talk about a tendency relationship, not a cause-and-effect relationship.
Exercises 8 – 10:
What you should look for when evaluating an experiment:
→ Were the subjects randomly assigned to treatment groups?
→ Was there a control group of a comparison group?
→ Were the sample sizes reasonably large?
→ Do the results show a cause-and-effect relationship?
Read the abstracts of the two articles below. Write a few sentences evaluating these articles using the guidelines above.
The study ‘Semantic Memory Functional MRI and Cognitive Function After Exercise Intervention in Mild Cognitive Impairment” (Journal of Alzheimer’s Disease, August 2013) was performed to see if exercise would increase memory retrieval in older adults with mild cognitive impairment (associated with early memory loss).
While there was a control group of nonimpaired adults, the sample sizes are too small to demonstrate the variation in the responses. Also, the subjects were not randomly assigned to treatment groups. Therefore, no cause-and-effect relationship can be shown with this study. The authors correctly stated, “These findings suggest exercise may improve … semantic memory retrieval in MCI…”
The article “Effects of Bracing in Adolescents with Idiopathic Scoliosis’ (New England Journal of Medicine, October 2013) reports on the role of bracing patients with adolescent idiopathic scoliosis (curvature of the spine) for prevention of back surgery.
Researchers conducted a study of one hundred sixteen (reasonably large enough) adolescent patients with scoliosis in which each patient was randomly assigned to either a treatment where the patient wore a brace or a treatment where the patient’s progress was observed. The treatment where the patients’ progress was observed is a control group.
Therefore, the conclusion that wearing a brace significantly decreased the progression of high-risk curves toward the need for surgery is accurate. The researchers also examined what the treatment effects were if the patients were all wed to choose their treatment (which is not an experiment).
View the report by Tom Bemis (Market Watch, Wall Street Journal, August 13, 2013) about the type of car driven by a person and the person’s driving behavior.
Is the title “BMW Drivers Really Are Jerks” an accurate title for these reported studies? Why or why not? If not, suggest a better title.
The title may imply that because o person drives a BMW, this causes the person to use bad driving habits. Since these studies are observational studies and not experiments, this is inaccurate. A more appropriate title would be “BMW Drivers Tend to Have Bad Driving Behaviors.”
Eureka Math Algebra 2 Module 4 Lesson 30 Problem Set Answer Key
Read the following articles and summaries. Write a few sentences evaluating each one using the guidelines given in the lesson.
The article “Emerging Technology” (Discover Magazine, November 2005) reports a study on the effect of “infomania” on IQ scores.
This article discusses two groups of people: one who had to check email and respond to 1M while testing and the other who was not distracted by email or IM. It does not specify that subjects were randomly assigned to the 2 groups. Also, the sample sizes were not stated. Therefore, based on this article, it would not be reasonable to state a cause-and-effect relationship.
In The New England Journal of Medicine, October 2013, the article “Increased Survival in Pancreatic Cancer with nab-Paclitaxel Plus Gemcitabine” reports on an experiment to test which treatment, nab-paclitaxel plus gemcitabine or gemcitabine alone, is the most effective in treating advanced pancreatic cancer.
The article states that pancreatic cancer patients were randomly assigned to 2 groups. The sample sizes (431 and 430) were large enough to observe the variation in responses. The standard treatment of gemcitabine alone was the comparison group. The conclusion, that the treatment group of nab-paclitaxel plus gemcitabine significantly improved the overall survival rate, is accurate.
Doctors conducted a randomized trial of hypothermia in infants with a gestational age of at least 36 weeks who were admitted to the hospital at or before six hours of age with either severe acidosis or perinatal complications and resuscitation at birth and who had moderate or severe encephalopathy. The trial “Whole-Body Hypothermia for Neonates with Hypoxic – Ischemic Encephalopathy” tested two treatments, standard care, and whole-body cooling for 72 hours.
The article states that the infants were randomly assigned to usual care (the control group – 106 infants) or whole-
body cooling (102 infants). Thus, the sample sizes were large enough to observe the variation in responses. The conclusion, that whole-body cooling reduces the risk of death or disability in infants with moderate or severe encephalopathy, is accurate.
Eureka Math Algebra 2 Module 4 Lesson 30 Exit Ticket Answer Key
What are the aspects of a well-designed experiment that show a causal relationship?
The use of a control group or a comparison group sets a baseline for the treatment effect. The use of random assignment evenly spreads the effects of extraneous variables into the treatment groups. Thus, any significant difference between the treatment groups can be attributed to the treatment, and you can conclude that the treatment is the cause of the observed difference.