Statistics Study Design

The population of a town is divided into three age categories. A random sample of each category is surveyed about voting choices. This type of sampling is called

• cluster sampling.

• stratified sampling.

• simple random sampling.

• systematic random sampling.

News cameras take an overhead picture of a part of a crowd at an outdoor event. Journalists then count the number of people in the picture and use the sample to estimate the total number of people in the crowd. This process is an example of

• random sampling.

• stratified sampling.

• systematic random sampling.

• cluster sampling.

A teacher asks students to list the math lessons they learned on nine random school days in the past month. She evaluates the students’ performance on this assignment to get a general picture of how well students are taking notes. This teacher’s method is an example of

• systematic random sampling.

• simple random sampling.

• convenience sampling.

• stratified sampling.

A statistics teacher decides to compare this year's students to all those she has taught over the history of the course. She will use the students' examination performances as the method of comparison. Which of the following is true in this context?

• The mean performance of this year's students is a parameter.

• The mean performance of this year's students is a statistic.

• The mean of all except this year's students is a parameter.

• The mean of all students is a statistic.

• None of these is true.

Left-handedness is the preference for the left hand over the right for everyday activities such as writing. Studies indicate that about 93% of the population may be characterized as right-handed. Researchers would like to conduct a study to determine if left-handed teens differ significantly in their ability to memorize facts than right-handed teens. Suppose the researchers concluded that the average number of words memorized by left-handed teens was statistically significantly higher than the average number memorized by right-handed teens. In this context, statistically significant means that:

• the number of words memorized by left-handed students exceeded the number memorized by right-handed students.

• the average number of words memorized by left-handed students exceeded the average number memorized by right-handed students.

• right-handed students tend to not do as well as left-handed students in memorizing words.

• it would be unlikely to observe an average difference as large as was observed by chance variation.

• a randomized, controlled experiment was conducted.

A market research company wishes to find out whether the population of students at a university prefers Starbucks or Dunkin Donuts. A random sample of students is selected, and each student is asked first to try both but the order they try them is randomly decided with a coin toss (heads: Starbucks, then Dunkin. tails: vice versa). They then indicate which brand they prefer. This is an example of

• completely randomized experiment

• an observational study

• blocked experiment

• matched pairs experiment

Dentists want to know if a fluoride mouth wash will help prevent cavities. After 6 months, they will compare the number of cavities in those who used the mouth wash versus those who did not. Which is an example of a matched pairs design for this experiment?

• Dentists sort 40 patients into groups based on age, such as 10-14, 15-20, 21-26, and 26-30. Half of the patients in each group are given the mouth wash, half are not.

• Dentists sort 50 patients into pairs that are the same age. 1 person is given the mouth wash and 1 is not.

In order to perform an experiment using 60 members of a gym, I first divide the list of members into men and women because I feel that the results will be different based on gender. I then randomly choose 30 men and 30 women. I assign half of the men to the treatment group and half to the control group. I repeat this procedure with the women. This is an example of a:

• completely randomized experiment

• blocked experiment

• matched pairs experiment

• observational study

What is confounding in AP Statistics survey design and how does it impact the validity of the study?

• Confounding in AP Statistics survey design refers to a situation where the effect of a confounding variable is mixed with the effect of the independent variable, making it difficult to determine the true cause of the observed relationship. It impacts the validity of the study by introducing bias and making it challenging to establish a cause-and-effect relationship between the independent and dependent variables.

• Confounding in AP Statistics survey design refers to a situation where the effect of a confounding variable is negligible and does not impact the validity of the study.

• Confounding in AP Statistics survey design refers to a situation where the effect of a confounding variable is easily separated from the effect of the independent variable, ensuring the validity of the study.

• Confounding in AP Statistics survey design refers to a situation where the effect of a confounding variable is completely independent of the effect of the independent variable, enhancing the validity of the study.

Statistics teachers often debate the best order in which to teach topics. One group of teachers likes to teach design of studies first. Another group likes to begin with data analysis. To see which order is more effective in preparing students for the AP Exam, an experiment was proposed. A large group of teachers, each of whom teaches two sections of statistics, volunteered to be part of the experiment. Each teacher will randomly assign one of their classes to beign with design, and the other to begin with data analysis. Which is the correct description of this design?

• The experimental units are the classrooms, the blocks are the teachers, and the response variable is the difference in average AP Exam score for each of the teacher's classes.

• The experimental units are the teachers, there are no blocks, and the response variable is the average AP Exam score for each teacher.

• The experimental units are the individual students, the blocks are the classrooms, and the response variable is each individual student's AP Exam score.

• The experimental units are the individual students, the blocks are the teachers, and the response variable is the average AP Exam score for each classroom

• The experimental units are the order of the topics, the blocks are the teachers, and the response variable is the average AP Exam score for all students who used each order of topics.