Review Unit #5 - 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.

Tags

CCSS.HSS.IC.B.3

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

Tags

CCSS.HSS.IC.B.3

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.

Tags

CCSS.7.SP.A.1

CCSS.HSS.IC.A.1

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

Tags

CCSS.HSS.IC.B.3

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.

Tags

CCSS.HSS.IC.B.3

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

Tags

CCSS.7.SP.A.1

CCSS.HSS.IC.A.1

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

Tags

CCSS.HSS.IC.B.3

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.

Tags

CCSS.HSS.IC.B.3

In a recent poll of 1,500 randomly selected eligible voters, only 525 (35 percent) said that they did not vote in the last election. However, a vote count showed that 80 percent of eligible voters actually did not vote in the last election. Which of the following types of bias is most likely to have occurred in the poll?

• Nonresponse bias

• Sampling bias

• Selection bias

• Response bias

• Undercoverage bias

Tags

CCSS.HSS.IC.B.3

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.

Tags

CCSS.HSS.IC.B.3