Sampling and Experimentation

A program exists to encourage more middle school students to major in math and science when they go to college. The organizers of the program want to estimate the proportion of students who, after completing the program, go on to major in math or science in college. The organizers will select a sample of students from a list of all students who completed the program. Which of the following sampling methods describes a stratified random sample?

• Select all female students on the list.

• Randomly select 50 students on the list.

• Randomize the names on the list and then select every tenth student on the randomized list.

• Randomly select 25 names from the female students on the list and randomly select 25 names from the male students on the list.

• Randomly select 50 students on the list who are attending college.

A pharmaceutical company manufactures medicine to reduce pain caused by migraine headaches. The company is investigating whether a new medicine is more effective in reducing pain than the current medicine. A random sample of 500 participants who experience migraines was selected, and the participants were randomly assigned to one of two groups of equal size. The first group received the current medicine and the second group received the new medicine. When a participant experienced a migraine, he or she was instructed to take the medicine and, 15 minutes after taking the medicine, to rate the pain relief on a scale from 1 to 10, with 1 being no relief to 10 being complete relief. At the end of six months, the average pain relief for each participant was calculated. Which of the following is the best description of the study?

• An experiment using a completely randomized design

• An experiment using a matched-pairs design

• An observational study using a simple random sample

• An observational study using a cluster sample

• An observational study using a stratified sample

The transportation department of a large city wants to estimate the proportion of residents who would use a system of aerial gondolas to commute to work. The gondolas would be part of the city’s effort to relieve traffic congestion. The department asked a random sample of residents whether they would use the gondolas. The residents could respond with yes, no, or maybe. Which of the following is the best description of the method for data collection used by the department?

• A census

• A sample survey

• An experiment with a completely randomized design

• An experiment with a randomized block design

• An experiment with a matched-pairs design

As part of a study on facility needs, the administrators of a university wanted to estimate the percent of students who use the exercise facilities on a regular basis. From the 34,000 students who attend the university, a random sample of 370 male students and 400 female students was selected. Of the 770 students selected, 493 students indicated that they use the exercise facilities on a regular basis. What are the population and the sample of the study?

• The population is the 770 students who were selected, and the sample is the 493 students who indicated that they use the exercise facilities on a regular basis.

• The population is the 770 students who were selected, and the sample is whether each student in the survey uses the exercise facility on a regular basis.

• The population is the 34,000 students who attend the university, and the sample is whether each student in the survey is male or female.

• The population is the 34,000 students who attend the university, and the sample is the 770 students who were selected.

• The population is the 34,000 students who attend the university, and the sample is the 493 students who indicated that they use the exercise facilities on a regular basis.

Researchers conducted a study to investigate the effects of soft drink consumption on fat stored in muscle tissue. From a sample of 80 adult volunteers, 40 were randomly assigned to consume one liter of a soft drink each day. The remaining 40 were asked to drink one liter of water each day and not to consume any soft drinks. At the end of six months, the amount of fat stored in each person’s muscle tissue was recorded. The people in the group who drank the soft drink had, on average, a higher percentage of fat stored in the tissue than the people who drank only water. Which of the following is the most appropriate conclusion?

• There is evidence that consuming soft drinks causes more fat storage in muscle tissue than drinking only water, and the conclusion can be generalized to all adults.

• There is evidence that consuming soft drinks causes more fat storage in muscle tissue than drinking only water, and the conclusion can be generalized to all people who consume soft drinks.

• There is evidence that consuming soft drinks causes more fat storage in muscle tissue than drinking only water, and the conclusion can be generalized to adults similar to those in the study.

• Although cause-and-effect cannot be established, there is an association between consuming soft drinks and fat storage in muscle tissue for the population of all adults.

• Although cause-and-effect cannot be established, there is an association between consuming soft drinks and fat storage in muscle tissue for the population of all adults who consume soft drinks.

Researchers wanted to investigate whether babies have a sense of right and wrong. They showed each of 60 babies a puppet show in which a red puppet was trying to open a heavy box lid. A second puppet, called the helper, would try to help the red puppet open the box, while a third puppet, called the hinderer, would try to slam the box lid down. After watching the show, each baby was presented with a tray containing the helper puppet and the hinderer puppet, and the researchers recorded which puppet the baby reached for. The researchers wanted to determine whether the babies would reach for the helper puppet more than for the hinderer puppet. As part of the show, a green puppet and a yellow puppet served as the helper and hinderer. For each baby, a coin was tossed to determine which color would serve which role. Which of the following is the most important reason for the random assignment of color to role in the study?

• Slamming the lid might cause wear on the hinderer puppet after 60 shows. The random assignment of color to role permits more even wear between the helper and the hinderer.

• The puppeteer might grow tired of doing the same show with the same puppet colors. The random assignment of color to role keeps the show fresh for each performance.

• If the same role is played by the same color puppet, the babies might show a preference for the color instead of a preference for the role.

• The random assignment of color to role allows the researchers to determine if one color is better than another in teaching babies right from wrong.

• Boys and girls might prefer different colors. The random assignment of color to role ensures that the show is equally accessible to boys and girls.

A florist wanted to investigate whether a new powder added to the water of cut flowers helps to keep the flowers fresh longer than just water alone. For a shipment of roses that was delivered to the store, the florist flipped a coin before placing each rose in its own individual container with water. If the coin landed heads up, the rose was placed in water with the new powder; otherwise, the rose was placed in water alone. Which of the following is the best description of the method used by the florist?

• A census, because all roses are assigned to a container

• An experiment with a completely randomized design

• An experiment with a blocked design, with blocking by type of water

• An experiment with a matched-pairs design

• An observational study

Some contact lens wearers report problems with dryness in their eyes. A study was conducted to evaluate the effectiveness of a new eye-drop solution to relieve dryness for contact lens wearers. Twenty-five volunteers who wore contact lenses agreed to use the new solution for one month. At the end of the month, 36 percent of the volunteers reported that the new solution was effective in relieving dryness. The company that produced the new eye-drop solution concluded that using the new solution is more effective in relieving dryness than using no solution. Which of the following best explains why the study does not support such a conclusion?

• The sample size was too small.

• The study had no control group.

• The participants were volunteers.

• The participants self-reported the frequency with which they used the new solution.

• The participants self-reported the effectiveness of the new solution.

At a large conference of teachers from a variety of subjects, a random sample of 50 mathematics teachers attending the conference was selected. Among the selected mathematics teachers, 28 percent had taken one or more courses in statistics. For which of the following populations is 28 percent a reasonable estimate of the percentage of those who have taken one or more courses in statistics?

• All mathematics teachers

• All mathematics teachers who attended the conference

• All mathematics teachers who have taken one or more courses in statistics

• All teachers who attended the conference

• All teachers

A well-designed experiment should have which of the following characteristics?

I. Subjects assigned randomly to treatments

II. A control group or at least two treatment groups

III. Replication

• I only

• I and II only

• I and III only

• II and III only

• I, II and III