Houston
1. Consider this investigative question: For U.S. adults, is more weekly exercise associated with a lower resting heart rate compared to less weekly exercise? What is the explanatory variable? What is the response variable? (Lesson 2.1)
Explanatory: Weekly exercise
Response: Lower Resting Heart Rate
3. A researcher randomly assigns 40 volunteers to either walk for 30 minutes or sit quietly for 30 minutes every day for two weeks, then compares their stress ratings. What type of study is this (experiment, observational study using a survey, or observational study using direct observation)? Explain how you know. (Lesson 2.1)
Experiment. The researcher randomly assigned volunteers to a treatment (walking or sitting quietly), so the conditions were imposed on the subjects.
8. To generalize results to an entire target population, what must be true? (Lesson 2.1)
The sample must be randomly selected from the whole target population.
14. Name one sampling method that is not a random sampling method. (Lesson 2.2)
12. A hospital divides its patients into two groups: inpatients and outpatients. It then randomly selects 30 patients from each group to survey. What type of sampling method is this? (Lesson 2.2)
Stratified random sample.
2. There are three main components of a good investigative question. Name all three. (Lesson 2.1)
Variables, direction, and population
4. Give one example of a survey. (Lesson 2.1)
Answers should involve something with subjects responding to a question.
**SEE GRAPH ON #9** What conclusion is appropriate about whether the medication caused a reduction in illness? Explain. Then explain whether these results can be generalized to children.
Because participants were randomly assigned to the medication or the placebo, extraneous variables are balanced between the groups, so we can conclude the medication caused a reduction in illness (42 vs. 310 who became ill, and 2 vs. 36 who were hospitalized). The results cannot be generalized to children because only adults were in the study.
**See #16**
16. What are the experimental units in this study? (Lesson 2.4)
The 40 athletes
13. A school administrator wants to estimate the proportion of all students at the school who play video games at least once a week. He surveys only the members of the school's gaming club. How will this sampling method most likely affect his estimate? Explain. (Lesson 2.3)
It will most likely overestimate the true proportion. Members of the gaming club are more likely to play video games than the typical student, so the sample is not representative of all students.
5. What is a confounding variable? (Lesson 2.1)
An extraneous variable that is associated with both the explanatory and response variables and creates doubt about a causal connection between them.
6. A study finds that students who eat breakfast every morning earn higher test scores than students who do not. Name one variable that is likely to confound this relationship, and explain why. (Lesson 2.1)
Answers vary. Examples: family income, amount of sleep, or how motivated or health-conscious the student is. The explanation should say the variable is related to both eating breakfast and test scores, so it could be the true cause of the difference.
10. A town has 800 residents. Describe how you could take a simple random sample of 40 residents. (Lesson 2.2)
Number all 800 residents from 1 to 800. Use a random number generator to select 40 different numbers (skipping repeats). The residents with those numbers make up the sample. (Equivalent method: names on identical slips of paper, drawn from a hat without replacement.)
11. A state numbers its 60 public high schools from 1 to 60, randomly selects 5 of the schools, and surveys every student in those 5 schools. What type of sampling method is this? (Lesson 2.2)
Cluster random sample.
15. A class took many random samples of students from their school and recorded the mean number of hours of sleep from each sample. The sample means were centered at the true mean for the school, but they were spread out widely from sample to sample. Describe this sampling method using the terms biased or unbiased and precise or imprecise. (Lessons 2.2 and 2.3)
Accurate (unbiased) but imprecise. The sample means are centered at the true mean (unbiased), but they vary a lot from sample to sample (imprecise).
19. Name two principles of good experimental design. (Lesson 2.4)
Any two of: comparison of at least two treatment groups, random assignment of treatments to experimental units, replication, direct control of extraneous variables.
7. What is the difference between a census and a sample? (Lesson 2.1)
A census measures every individual in the population. A sample measures only a subset of the population.
**SEE GRAPH**
20. In an experiment, researchers gave identical cookies to taste testers. Half of the testers were told the cookies were "homemade," and half were told the cookies were "store-bought." Testers rated each cookie. The graph shows the mean ratings (on a 1–7 scale). (Lesson 2.4) According to the graph, how much higher was the mean freshness rating for the "homemade" cookies than for the "store-bought" cookies?
1.4 points
17. What is the main purpose of randomly assigning athletes to the two groups? (Lesson 2.4)
To balance extraneous variables between the two groups, so that they do not confound the relationship between stretching and run time. This makes a cause-and-effect conclusion possible.
21. In a double-blind study of a new migraine pill, who does not know which treatment each subject received? (Lesson 2.5)
Both the subjects and the researchers evaluating them.
22. What is the main purpose of giving the control group a placebo? (Lesson 2.5)
To control for the placebo effect, so that any difference between the groups can be attributed to the treatment itself and not to the subjects' expectations.
23. A school surveys its students and collects the following data: full name, date of birth, bus route number, and a rating of the cafeteria food (1 to 10). Which two data points would be considered indirect information (information that could identify someone only when combined with other data)? Explain. (Lesson 2.5)
Date of birth and bus route number. Neither could identify a student by itself, but together they could be used to pick out one individual. (Full name is direct information, and the food rating is not identifying.)
24. What does informed consent mean in a study? (Lesson 2.6)
Participants are told about the study and are then allowed to decide for themselves whether to participate.
18. How does this study use replication? (Lesson 2.4)
Each treatment (stretching or not stretching) is used with many experimental units: 20 athletes in each group. This reduces the impact of chance variation, making a treatment effect easier to detect.
25. Two neighboring counties have very similar populations and habits. One county bans plastic shopping bags, and the other does not. Researchers compare the amount of litter collected in parks near the border in each county. Why is this considered a natural experiment? (Lesson 2.6)
The researchers did not assign the ban to the counties. The border created natural treatment groups, and because parks near the border are otherwise similar, the groups are as good as randomly assigned. Any difference in litter can be attributed to the bag ban.