1. Intro to Stats and Collecting Data

Intro to Stats

1. Intro to Stats and Collecting Data

Intro to Stats

2:24 minutes

Problem 1.6.11e

Textbook Question

"Whiter Teeth An ad for Crest Whitestrips Premium claims that the strips will whiten teeth in 7 days and the results will last for 12 months. A researcher who wishes to test this claim studies 20 sets of identical twins. Within each set of twins, one is randomly selected to use Crest Whitestrips Premium in addition to regular brushing and flossing, while the other just brushes and flosses. Whiteness of teeth is measured at the beginning of the study, after 7 days, and every month thereafter for 12 months.

What might be an advantage of using identical twins as subjects in this experiment?"

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Understand the purpose of using identical twins in an experiment: identical twins share nearly the same genetic makeup, which helps control for genetic variability between subjects.

Recognize that by comparing one twin who uses the Crest Whitestrips Premium with the other twin who does not, the researcher can isolate the effect of the whitening strips more effectively.

Note that using identical twins reduces the influence of confounding variables related to genetics, such as natural tooth color or enamel properties, which might affect whitening results.

Consider that this design helps improve the internal validity of the experiment by controlling for genetic differences, making it easier to attribute differences in tooth whiteness to the treatment rather than genetic factors.

Summarize that the main advantage is controlling for genetic variation, which reduces variability in the data and increases the reliability of the comparison between treated and untreated groups.

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Key Concepts

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

Control of Genetic Variation

Using identical twins controls for genetic differences because twins share the same DNA. This reduces variability in traits like tooth color or enamel strength, allowing the researcher to isolate the effect of the whitening strips more accurately.

Paired Experimental Design

A paired design compares outcomes within matched pairs (twins), which increases statistical power by controlling for confounding variables. Each twin acts as a control for the other, minimizing the impact of external factors.

Random Assignment Within Pairs

Randomly assigning one twin to treatment and the other to control prevents selection bias. This ensures that differences in outcomes are likely due to the treatment rather than systematic differences between subjects.

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Textbook Question

College Survey In a national survey conducted by the Centers for Disease Control to determine health-risk behaviors among college students, college students were asked, “How often do you wear a seat belt when riding in a car driven by someone else?” The frequencies were as follows:

g. Suppose that a representative from the Centers for Disease Control says, “52.7% of college students surveyed always wear a seat belt.” Is this a descriptive or inferential statement?

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Textbook Question

"Pharmacy A pharmaceutical company has developed an experimental drug meant to relieve symptoms associated with the common cold. The company identifies 300 adult males 25 to 29 years old who have a common cold and randomly divides them into two groups. Group 1 is given the experimental drug, while group 2 is given a placebo. After 1 week of treatment, the subjects report whether they still have cold symptoms, or not.

How are the factors that are not controlled dealt with?"

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Textbook Question

What type of experimental design is this?"

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Textbook Question

"Whiter Teeth An ad for Crest Whitestrips Premium claims that the strips will whiten teeth in 7 days and the results will last for 12 months. A researcher who wishes to test this claim studies 20 sets of identical twins. Within each set of twins, one is randomly selected to use Crest Whitestrips Premium in addition to regular brushing and flossing, while the other just brushes and flosses. Whiteness of teeth is measured at the beginning of the study, after 7 days, and every month thereafter for 12 months.

What are other factors (controlled or uncontrolled) that could affect the response variable?"

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Textbook Question

"Insomnia Researchers wanted to test the effectiveness of a new cognitive behavioral therapy (CBT) compared with both an older behavioral treatment and a placebo therapy for treating insomnia. They identified 75 adults with insomnia. Patients were randomly assigned to one of three treatment groups. Twenty-five patients were randomly assigned to receive CBT (sleep education, stimulus control, and time-in-bed restrictions), another 25 received muscle relaxation training (RT), and the final 25 received a placebo treatment. Treatment lasted 6 weeks, with follow-up conducted at 6 months. To measure the effectiveness of the treatment, researchers used wake time after sleep onset (WASO). CBT produced larger improvements than did RT or placebo treatment. For example, the CBT-treated patients achieved an average 54% reduction in their WASO, whereas RT-treated and placebo-treated patients, respectively, achieved only 16% and 12% reductions in this measure. Results suggest that CBT treatment leads to significant sleep improvements within 6 weeks, and these improvements appear to endure through 6 months of follow-up. 53 Source: Jack D. Edinger, PhD; William K. Wohlgemuth, PhD; Rodney A. Radtke, MD; Gail R. Marsh, PhD; Ruth E. Quillian, PhD. “Cognitive Behavioral Therapy for Treatment of Chronic Primary Insomnia,” Journal of the American Medical Association 285: 1856–1864, 2001

What type of experimental design is this?"

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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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