1. Intro to Stats and Collecting Data

Intro to Stats

1. Intro to Stats and Collecting Data

Intro to Stats

3:14 minutes

Problem 12.2.13b

Textbook Question

Efficacy of e-Cigs Do electronic cigarettes assist in helping individuals quit smoking? Researchers found 300 current smokers to volunteer for a study in which each was randomly assigned to one of three treatment groups. Group 1 received an electronic cigarette (e-cig) in which each cartridge contained 7.2 mg of nicotine, Group 2 received an e-cig that contained 5.4 mg of nicotine, and Group 3 received an e-cig that contained no nicotine. The subjects did not know which group they were assigned. During the course of the 52-week intervention, subjects dropped out of the study. At the end of the study 65 subjects remained in Group 1, 63 in Group 2, and 55 in Group 3. After 52 weeks, it was determined via questionnaire whether the subject quit smoking entirely. Results of the study are presented in the following table.

b. Researchers wanted to know whether electronic cigarettes may be used to help individuals abstain from cigarette smoking. What is the response variable? Is it qualitative or quantitative?

Verified step by step guidance

Step 1: Identify the response variable by understanding what the researchers are measuring as the outcome of the study. In this case, the researchers want to know if individuals quit smoking after using electronic cigarettes.

Step 2: The response variable is the smoking cessation status of each participant after 52 weeks, which is whether the participant 'Quit' or 'Did Not Quit' smoking.

Step 3: Determine the type of the response variable. Since the response variable categorizes participants into groups based on their smoking status (Quit or Did Not Quit), it is a qualitative (categorical) variable.

Step 4: Summarize that the response variable is 'Smoking cessation status' and it is qualitative because it describes categories rather than numerical measurements.

Step 5: Note that this qualitative response variable is used to compare the effectiveness of different nicotine levels in electronic cigarettes across the three groups.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Response Variable

The response variable is the main outcome measured in a study to assess the effect of treatments. In this question, it is whether the subjects quit smoking or not after 52 weeks. Identifying the response variable helps focus the analysis on what the researchers want to explain or predict.

Qualitative vs. Quantitative Variables

Variables can be qualitative (categorical) or quantitative (numerical). Qualitative variables describe categories or groups, such as 'quit' or 'did not quit,' while quantitative variables represent measurable amounts. Here, the response variable is qualitative because it categorizes subjects based on smoking cessation status.

Random Assignment and Blinding

Random assignment ensures each subject has an equal chance of being placed in any treatment group, reducing bias. Blinding means subjects do not know their group, preventing their knowledge from influencing outcomes. Both methods improve the validity of conclusions about the effect of e-cigarettes on quitting smoking.

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Textbook Question

"Designing an Experiment Researchers want to know if there is a link between hypertension (high blood pressure) and consumption of salt. Past studies have indicated that the consumption of fruits and vegetables offsets the negative impact of salt consumption. It is also known that there is quite a bit of person-to-person variability in the ability of the body to process and eliminate salt. However, no method exists for identifying individuals who have a higher ability to process salt. The U.S. Department of Agriculture recommends that daily intake of salt should not exceed 2400 milligrams (mg). The researchers want to keep the design simple, so they choose to conduct their study using a completely randomized design.

Name three factors that have been identified."

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Textbook Question

Putting It Together: Online Homework Keeping students engaged in the learning process greatly increases their chance of success in a course. Traditional lecture-based math instruction has given way to a more student-engaged approach where students interact with the teacher in class and receive immediate feedback to their responses. The teacher presence allows students, when incorrect in a response, to be guided through a solution and then immediately be given a similar problem to attempt. A researcher conducted a study to investigate whether an online homework system using an attempt—feedback— reattempt approach improved student learning over traditional pencil-and-paper homework. The online homework system was designed to increase student engagement outside class, something commonly missing in traditional pencil-and-paper assignments, ultimately leading to increased learning.The study was conducted using two first-semester calculus classes taught by the researcher in a single semester. One class was assigned traditional homework and the other was assigned online homework that used the attempt—feedback—reattempt approach. The summaries are based on data from the study.

d. Explain why assigning homework type to entirely separate classes can confound the conclusions of the study.

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Textbook Question

f. What type of variable is letter grade? What level of measurement is letter grade? Do you think presenting the data in a table from A to F would be a better representation of the data than presenting it in a graph?

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Textbook Question

[DATA] Ramp Metering [See Problem 13 in Section 11.3.] Ramp metering is a traffic engineering idea that requires cars entering a freeway to stop for a certain period of time before joining the traffic flow. The theory is that ramp metering controls the number of cars on the freeway and the number of cars accessing the freeway, resulting in a freer flow of cars, which ultimately results in higher speeds on the road. To test whether ramp metering is effective in reducing travel times, engineers in Minneapolis, Minnesota, conducted an experiment in which a section of freeway had ramp meters installed on the on-ramps. A random sample of 15 cars on the highway for a Monday at 6 P.M. with the ramp meters on and a second random sample of 15 cars on a different Monday at 6 P.M. with the meters off resulted in the following speeds (in miles per hour).

a. What is the explanatory variable in this study? What is the response variable?

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Textbook Question

Efficacy of e-Cigs Do electronic cigarettes assist in helping individuals quit smoking? Researchers found 300 current smokers to volunteer for a study in which each was randomly assigned to one of three treatment groups. Group 1 received an electronic cigarette (e-cig) in which each cartridge contained 7.2 mg of nicotine, Group 2 received an e-cig that contained 5.4 mg of nicotine, and Group 3 received an e-cig that contained no nicotine. The subjects did not know which group they were assigned. During the course of the 52-week intervention, subjects dropped out of the study. At the end of the study 65 subjects remained in Group 1, 63 in Group 2, and 55 in Group 3. After 52 weeks, it was determined via questionnaire whether the subject quit smoking entirely. Results of the study are presented in the following table.

c. To what population do the results of this study apply?

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Textbook Question

Putting It Together: Women, Aspirin, and Heart Attacks In a famous study by the Physicians Health Study Group from Harvard University from the late 1980s, 22,000 healthy male physicians were randomly divided into two groups; half the physicians took aspirin every other day, and the others were given a placebo. Of the physicians in the aspirin group, 104 heart attacks occurred; of the physicians in the placebo group, 189 heart attacks occurred. The results were statistically significant, which led to the advice that males should take an aspirin every other day in the interest of reducing the chance of having a heart attack. Does the same advice apply to women?

In a randomized, placebo-controlled study, 39,876 healthy women 45 years of age or older were randomly divided into two groups. The women in group 1 received 100 mg of aspirin every other day; the women in group 2 received a placebo every other day. The women were monitored for 10 years to determine if they experienced a cardiovascular event (such as heart attack or stroke). Of the 19,934 in the aspirin group, 477 experienced a heart attack. Of the 19,942 women in the placebo group, 522 experienced a heart attack. Source: Paul M. Ridker et al. “A Randomized Trial of Low-Dose Aspirin in the Primary Prevention of Cardiovascular Disease in Women.” New England Journal of Medicine 352:1293–1304.

e. How does randomization deal with the explanatory variables that were not controlled in the study?

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Textbook Question

Distinguish between sampling and nonsampling error.

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Textbook Question

Define each of the following. Lurking variable

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