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.

True or False: all samples lead to a good prediction about an entire population.

• True

• False

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

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 survey was administered to parents of high school students in a certain state to see if the parents thought the students’ academic needs were being met. To select the sample, the parents were divided into two groups— one group of parents who live in cities with populations of more than 100,000 and the other group of parents who live in cities with populations less than or equal to 100,000. A random sample of 100 parents from each group was taken. Which of the following statements about the sample of 200 parents is true?

• It is a convenience sample because the sample of parents was easily obtained.

• It is a stratified random sample because parents were randomly selected from each group.

• It is a random cluster sample because parents were randomly selected from each group.

• It is a random cluster sample because groups of high schools were randomly selected.

• It is a systematic sample because the parents were systematically divided into two groups.

An experiment will be conducted to determine whether children learn their multiplication facts better by practicing with flash cards or by practicing on a computer. Children who volunteer for the experiment will be randomly assigned to one of the two treatments. Because the children’s gender may affect the outcome, there will be blocking by gender. After practice, the children will be given a test on their multiplication facts. Why will it be impossible to conduct a double-blind experiment?

• The experimenter will know whether the child is a boy or a girl and whether he or she used flash cards or the computer.

• The child will know whether he or she is a boy or a girl.

• The child will know whether he or she used flash cards or the computer.

• The person who grades the tests will know whether the child was a boy or a girl.

• The person who grades the tests will know whether the child used flash cards or the computer.

Which of the following distinguishes an observational study from a randomized experiment?

• In an observational study volunteers are always used, whereas in a randomized experiment a random sample is always taken from the population.

• In an observational study a random sample is always taken from the population, whereas in a randomized experiment volunteers are always used.

• In an observational study treatments are not randomly assigned, whereas in a randomized experiment treatments are randomly assigned.

• In an observational study a control group is never used, whereas in a randomized experiment a control group is always used.

• An observational study can be double-blind, whereas a randomized experiment can only be single-blind because the experimenter determines who is randomly assigned to each treatment.