AP Statistics Gathering Data

A large simple random sample of people aged nineteen to thirty living in the state of Colorado was surveyed to determine which of two smartphones just developed by a new company was preferred. To which of the following populations can the results of this survey be safely generalized?

• Only people aged nineteen to thirty living in the state of Colorado who were in this survey

• Only people aged nineteen to thirty living in the state of Colorado

• All people living in the state of Colorado

• Only people aged nineteen to thirty living in the United States

• All people living in the United States

A researcher conducted an experiment to study the effects of an herbal supplement on the duration of the common cold. From a sample of 50 people who had a cold, the researcher assigned 25 people to take the supplement each day. The other 25 people were asked to drink water each day and were not given the supplement. The researcher recorded the number of days the cold lasted for each person. What are the experimental units of the study?

• All people with a cold

• The 25 people who were given the herbal supplement

• The sample of 50 people who had a cold

• The 25 people who were asked to drink water and were not given the supplement

• The recorded number of days that the cold lasted for each person

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 researcher wanted to estimate the average amount of money spent on extracurricular activities per school in a certain region. The researcher randomly selected 20 public schools and 20 private schools in the region to use for a sample. Which of the following best describes the type of sample that was taken?

• A census

• A cluster sample

• A convenience sample

• A simple random sample

• A stratified random sample

To estimate the percent of red marbles in a large bag of marbles, Margo will use the following sampling method. She will randomly select a marble, record its color, put it back into the bag, shake the bag to thoroughly mix the marbles, and then repeat those steps. She will perform the procedure many times. What type of sampling method is Margo using?

• Cluster sampling

• Stratified random sampling

• Systematic random sampling

• Random sampling with replacement

• Random sampling without replacement

A program that was intended to cure a person’s fear of spiders was offered at a local zoo. Volunteers with a fear of spiders participated in the program, which included holding a spider for 15 minutes. One month after they completed the program, the participants were contacted and surveyed about the program. Over 90 percent of the participants claimed they were cured of their fear of spiders. Based on the description of the program, which of the following statements is true?

• Because over 90% of the participants claimed to be cured, the results prove that holding a spider

  will cure a person’s fear of spiders.

• Because over 90% of the participants claimed to be cured, the results can be generalized to the

  population of all people who have a fear of spiders.

• Because the participants were self-selected, a person’s desire to be cured could be a confounding

  variable.

• Because the participants were volunteers, the study is a census of all people in the local area who

  have a fear of spiders.

• Because participants held a spider for 15 minutes, the study is an experiment and the results can

  be generalized to the population of all people who have a fear of spiders.

A researcher conducting a telephone survey is concerned about possible sources of bias. Of the following, which is the best example of nonresponse bias?

• People without telephones are overlooked in the sampling procedure used to determine who is

  surveyed.

• Many of the people selected to participate in the survey who do not respond might have opinions

  different from those who do respond.

• People might be uncomfortable with the survey questions and, as a result, might not always

  respond to those questions truthfully.

• The behavior of the interviewer leads people to respond in a certain way

• The wording of the questions in the survey leads people to respond in a certain way.

Which of the following does not describe a sampling method that has a potential source of

voluntary response bias for the administration of a survey about college athletics at a university?

• Giving the survey to 30 students selected at random from each of the eight dorms on campus

• Giving the survey to the first 50 students who call the university radio station after the broadcaster

  announces the survey on air

• Giving the survey to any student who stops at a table set up in the student union after the survey is

  advertised

• Giving the survey to all students who respond to an advertisement in the student newspaper

• Giving the survey to physical education majors who receive extra credit for completing the survey

A dog food company wishes to test a new high-protein formula for puppy food to determine whether it promotes faster weight gain than the existing formula for that puppy food. Puppies participating in an experiment will be weighed at weaning (when they begin to eat puppy food) and will be weighed at one-month intervals for one year. In designing this experiment, the investigators wish to reduce the variability due to natural differences in puppy growth rates. Which of the following strategies is most appropriate for accomplishing this?

• Block on dog breed and randomly assign puppies to existing and new formula groups within each

  breed.

• Block on geographic location and randomly assign puppies to existing and new formula groups

  within each geographic area.

• Stratify on dog breed and randomly sample puppies within each breed. Then assign puppies by

  breed to either the existing or the new formula.

• Stratify on geographic location of the puppies and randomly sample puppies within each

  geographic area. Then assign puppies by geographic area to either the existing or the new formula

• Stratify on gender and randomly sample puppies within gender groups. Then assign puppies by

  gender to either the existing or the new formula.

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