AP Stats Designing a Study

Biased or Random?

Chloe and Danna want to determine the favorite subject of all students in the middle school. So they place every middle school student's name in a bucket and choose 30 to poll.

• Biased sample

• Random sample

You want to take a simple random sample (SRS) of 50 of the 816 students who live in a dormitory on campus. You label the students 001 to 816 in alphabetical order. In the table of random digits, you read the entries (shown in the image).

The first three students in your sample have labels

• 955, 929, 400

• 400, 769, 769

• 559, 294, 007

• 929, 400, 769

• 400, 769, 335

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

Are dogs better at tracking the movements of brightly colored objects? Fifteen experienced “disk dogs” who have been trained to catch flying disks in mid-air are given the chance to catch a bright red disk or a plain white disk. Each disk is thrown 10 times for each dog, with the sequence of disks (red or white) determined randomly. The proportion of red disks caught to the proportion of white disks caught is compared for each dog. This is an example of a

• Simple random sample

• Stratified random sample.

• Completely randomized design.

• Matched pairs design.

• A block design, but not a matched pairs design.

A compact disc (CD) manufacturer wanted to determine which of two different cover designs for a newly released CD will generate more sales. The manufacturer chose 70 stores to sell the CD. Thirty-five of these stores were randomly assigned to sell CDs with one of the cover designs and the other 35 were assigned to sell the CDs with the other cover design. The manufacturer recorded the number of CDs sold at each of the stores and found a significant difference between the mean number of CDs sold for the two cover designs. Which of the following gives the conclusion that should be made based on the results and provides the best explanation for the conclusion?

• It is NOT reasonable to conclude that the difference in sales was caused by the different cover designs because this was not an experiment.

• It is NOT reasonable to conclude that the difference in sales was caused by the different cover designs because there was no control group for comparison.

• It is NOT reasonable to conclude that the difference in sales was caused by the different cover designs because the 70 stores were not randomly chosen.

• It is reasonable to conclude that the difference in sales was caused by the different cover designs because the cover designs were randomly assigned to stores.

• It is reasonable to conclude that the difference in sales was caused by the different cover designs because the sample size was large.

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.

To find out the average occupancy size of student-rented apartments, a researcher picks a simple random sample of 100 such apartments. Even after one follow-up visit, the interviewer is unable to make contact with anyone in 27 of these apartments. Concerned about nonresponse bias, the researcher chooses another simple random sample and instructs the interviewer to continue this procedure until contact is made with someone in a total of 100 apartments. The average occupancy size in the final 100-apartment sample is 2.78. Is this estimate probably too low or too high?

• Too high, because of undercoverage bias.

• Too high, because convenience samples overestimate average results.

• Too high, because voluntary response samples overestimate average results.

• Too low, because of undercoverage bias.

• Too low, because convenience samples overestimate average results.

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.

• Randomlyselect50studentsonthelistwhoareattendingcollege.

The manager of a public swimming pool wants to compare the effectiveness of two laundry detergents, Detergent A and Detergent B, in cleaning the towels that are used daily. As each dirty towel is turned in, it is placed into the only washing machine on the premises. When the washing machine contains 20 towels, the manager flips a coin to determine whether Detergent A or Detergent B will be used for that load. The cleanliness of the load of towels is rated on a scale of 1 to 10 by a person who does not know which detergent was used. The manager continues this experiment for many days. Which of the following best describes the manager’s study?

• A completely randomized design.

• A randomized block design with Detergent A and Detergent B as blocks.

• A randomized block design with the washing machine as the block.

• A matched-pairs design with Detergent A and Detergent B as the pair.

• An observational study.

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:

• randomized comparative design

• blocking design

• matched pairs design

• double blind simple random sample