AP Statistics Chapter 4 Study Tool | Example Problems

Hilary obtains a random sample of residents from her town. She surveys those residents on whether or not they consume Vitamin D and how much Vitamin D they get. She also measures their blood pressures. Suppose Hilary finds that among the people sampled, those who consume higher amounts of Vitamin D had significantly lower blood pressure than those who did not. Based on this study, we can safely say this result probably holds true for:

All residents in Hilary's town

Researchers working on a vaccine for HIV recruited over 16,000 volunteers for an experiment. Each volunteer was randomly assigned to receive monthly injections of either the vaccine or a placebo for a year. The researchers were curious if subjects who received the vaccine would be less likely to contract HIV than subjects who received the placebo. What does it mean for this experiment to be double-blind?

Both the subjects and the researchers are unaware of who is receiving the vaccine and who is receiving the placebo.

A study randomly assigned volunteers to one of two groups: One group was directed to use social media sites as they usually do. One group was blocked from social media sites. The researchers looked at which group tended to be happier. Which type of study method is this?

Experiment

Hilary wants to determine if any relationship exists between Vitamin D and blood pressure. Hilary obtains a random sample of residents from her town. She surveys those residents on whether or not they consume Vitamin D and how much Vitamin D they get. She also measures their blood pressure. Assuming the results show that higher Vitamin D consumption is correlated with lower blood pressure, and were found to be statistically significant, what conclusion can be drawn?

For all residents in Hilary's town, taking more Vitamin D will reduce the risk of high blood pressure.

A footwear company wants to test the effectiveness of its new insoles designed to prevent shin splints resulting from running. They hire a group of physical trainers and a statistician, who recruits 100 healthy adults between the ages of 18 and 24 to participate in a study. The statistician randomly assigns 50 of the adults to follow a weekly running schedule with the new insoles and the other 50 to the same running schedule with the existing insoles the company already sells. After 10 weeks, the statistician records the number of runners from each group that have developed shin splints. Neither the participants nor the researchers collecting the data knew which group had the new insoles and which group had the existing insoles. What is one reason for using this type of double-blind design?

It protects against some possible sources of bias.

Hilary recruits residents from her town who have physical exams scheduled in the next month with the local doctor's office. She randomly assigns the volunteers to either a Vitamin D supplement pill or a placebo pill. Participants do not know which pill they are taking. They have their blood pressures measured before the study begins and at the end of the study. Suppose Hilary finds that the group who took the Vitamin D supplements had a significant decrease in blood pressure, while the placebo group showed no significant change in blood pressure. Based on this study, we can safely say this result probably holds true for:

Just the residents in Hilary's study

A study took a random sample of adults and asked them about their bedtime habits. The data showed that people who drank a cup of tea before bedtime were more likely to go to sleep earlier than those who didn't drink tea. Which type of study method is this?

Observational study

A majority of people who receive surveys in the mail don't respond. Researchers were curious which type of reward would be most effective: send someone $10 after they mail a completed survey back, or send someone $5 with a survey as an advanced "thank you" that they can keep whether or not they participate. The researchers chose a random sample of 1200 adults and randomly assigned each of them to one of three groups: $10 after, $5 in advance, or no reward at all. They found that people in the $5 group were significantly more likely to send the survey back than people in either of the other groups. What conclusion can they draw from this study?

The $5 in advance caused the difference in survey completion.

A developer wants to know whether adding fibers to concrete used in paving driveways will reduce the severity of cracking, because any driveway with severe cracks will have to be repaired by the developer. The developer conducts a completely randomized experiment with 60 new homes that need driveways. Thirty of the driveways will be randomly assigned to receive concrete that contains fibers, and the other 30 driveways will receive concrete that does not contain fibers. After one year, the developer will record the severity of cracks in each driveway on a scale of 0 to 10, with 0 representing not cracked at all and 10 representing severely cracked. It is found that the amount of sunlight affects whether or not the driveway cracks. Given that particular areas typically receive more or less sunlight, how might a matched pairs design be used in this experiment?

driveways are ordered by how much sunlight they will receive, then we will go down the list assigning every other driveway to the experiment group and the rest to the control group

A company wants to study the effectiveness of a new pain relief medicine. They recruit 100 volunteers with chronic pain. Each subject takes the new pain relief medicine for a 2-week period, and a placebo for another 2-week period. Subjects don't know which pill is the actual medicine, and the order of the pills is randomly assigned for each subject. Researchers will measure the difference in the overall pain level for each subject. What type of experiment design is this?

matched pairs

Large doses of vitamin E apparently can reduce harmful side effects of bypass surgery in heart patients. A study involving 28 bypass patients found that the 14 patients who took vitamin E for two weeks before their operations had significantly better heart function after the procedure than the 14 patients who took placebos. Who/what are the experimental units/subjects in this experiment?

the 28 bypass patients

A developer wants to know whether adding fibers to concrete used in paving driveways will reduce the severity of cracking, because any driveway with severe cracks will have to be repaired by the developer. The developer conducts a completely randomized experiment with 60 new homes that need driveways. Thirty of the driveways will be randomly assigned to receive concrete that contains fibers, and the other 30 driveways will receive concrete that does not contain fibers. After one year, the developer will record the severity of cracks in each driveway on a scale of 0 to 10, with 0 representing not cracked at all and 10 representing severely cracked. What are the experimental units in the above experiment?

the 60 driveways that are being poured