Design of a Study: Sampling, Surveys, and Experiments Free Response Practice Problems for AP Statistics
Review the following concepts if necessary:
- Samples for AP Statistics
- Sampling Bias for AP Statistics
- Statistical Significance for AP Statistics
- Experiments and Observational Studies for AP Statistics
- You are interested in the extent to which ingesting vitamin C inhibits getting a cold. You identify 300 volunteers, 150 of whom have been taking more than 1000 mg of vitamin C a day for the past month, and 150 of whom have not taken vitamin C at all during the past month. You record the number of colds during the following month for each group and find that the vitamin C group had significantly fewer colds. Is this an experiment or an observational study? Explain. What do we mean in this case when we say that the finding was significant?
- Design an experiment that employs a completely randomized design to study the question of whether of not taking large doses of vitamin C is effective in reducing the number of colds.
- A survey of physicians found that some doctors gave a placebo rather than an actual medication to patients who experience pain symptoms for which no physical reason can be found. If the pain symptoms were reduced, the doctors concluded that there was no real physical basis for the complaints. Do the doctors understand the placebo effect? Explain.
- Explain how you would use a table of random digits to help obtain a systematic sample of 10% of the names on a alphabetical list of voters in a community. Is this a random sample? Is it a simple random sample?
- The Literary Digest Magazine, in 1936, predicted that Alf Landon would defeat Franklin Roosevelt in the presidential election that year. The prediction was based on questionnaires mailed to 10 million of its subscribers and to names drawn from other public lists. Those receiving the questionnaires were encouraged to mail back their ballot preference. The prediction was off by 19 percentage points. The magazine received back some 2.3 million ballots from the 10 million sent out. What are some of the things that might have caused the magazine to be so wrong (the same techniques had produced accurate predictions for several previous elections)? (Hint: Think about what was going on in the world in 1936.)
- Interviewers, after the 9/11 attacks, asked a group of Arab Americans if they trust the administration to make efforts to counter anti-Arab activities. If the interviewer was of Arab descent, 42% responded "yes" and if the interviewer was of non-Arab descent, 55% responded "yes." What seems to be going on here?
- There are three classes of statistics at your school, each with 30 students. You want to elect a simple random sample of 15 students from the 90 students as part of an opinion-gathering project for your social studies class. Describe a procedure for doing this.
- Question #1 stated, in part: "You are interested in the extent to which ingesting vitamin C inhibits getting a cold. You identify 300 volunteers, 150 of whom have been taking more than 1000 mg of vitamin C a day for the past month, and 150 of whom have not taken vitamin C at all during the past month. You record the number of colds during the following month for each group and find that the vitamin C group had significantly fewer colds." Explain the concept of confounding in the context of this problem and give an example of how it might have affected the finding that the vitamin C group had fewer colds.
- A shopping mall wants to know about the attitudes of all shoppers who visit the mall. On a Wednesday morning, the mall places 10 interviewers at a variety of places in the mall and asks questions of shoppers as they pass by. Comment on any bias that might be inherent in this approach.
- Question #2 asked you to design a completely randomized experiment for the situation presented in question #1. That is, to design an experiment that uses treatment and control groups to see if the groups differed in terms of the number of colds suffered by users of 1000 mg a day of vitamin C and those that didn't use vitamin C. Question #8 asked you about possible confounding variables in this study. Given that you believe that both general health habits and use of vitamin C might explain a reduced number of colds, design an experiment to determine the effectiveness of vitamin C taking into account general health habits. You may assume your volunteers vary in their history of vitamin C use.
- You have developed a weight-loss treatment that involves a combination of exercise and diet pills. The treatment has been effective with subjects who have used a regular dose of the pill of 200 mg, when exercise level is held constant. There is some indication that higher doses of the pill will promote even better results, but you are worried about side effects if the dosage becomes too great. Assume you have 400 overweight volunteers for your study, who have all been on the same exercise program, but who have not been taking any kind of diet pill. Design a study to evaluate the relative effects of 200 mg, 400 mg, 600 mg, and 800 mg daily dosage of the pill.
- You are going to study the effectiveness of three different SAT preparation courses. You obtain 60 high school juniors as volunteers to participate in your study. You want to assign each of the 60 students, at random, to one of the three programs. Describe a procedure for assigning students to the programs if
- you want there to be an equal number of students taking each course.
- you want each student to be assigned independently to a group. That is, each student should have the same probability of being in any of the three groups.
- A researcher wants to obtain a sample of 100 teachers who teach in high schools at various economic levels and has access to a list of teachers in several schools for each of the levels. She has identified four such economic levels (A, B, C, and D) that comprise 10%, 15%, 45%, and 30% of the schools in which the teachers work. Describe what is meant by a stratified random sample in this situation and discuss how she might obtain it.
- You are testing for sweetness in five varieties of strawberry. You have 10 plots available for testing. The 10 plots are arranged in two side-by-side groups of five. A river runs along the edge of one of the groups of five plots something like the diagram shown below (the available plots are numbered 1–10).
- Look at problem #14 again. It is the following year, and you now have only two types of strawberries to test. Faced with the same physical conditions you had in problem 14, and given that you are concerned that differing soil conditions (as well as proximity to the river) might affect sweetness, how might you block the experiment to produce the most reliable results?
- A group of volunteers, who had never been in any kind of therapy, were randomly separated into two groups, one of which received an experimental therapy to improve selfconcept. The other group, the control group, received traditional therapy. The subjects were not informed of which therapy they were receiving. Psychologists who specialize in self-concept issues evaluated both groups after training for self-concept, and the self-concept scores for the two groups were compared. Could this experiment have been double-blind? Explain. If it wasn't double-blind, what might have been the impact on the results?
- You want to determine how students in your school feel about a new dress code for school dances. One faction in the student council, call them group A, wants to word the question as follows: "As one way to help improve student behavior at school sponsored events, do you feel that there should be a dress code for school dances?" Another group, group B, prefers, "Should the school administration be allowed to restrict student rights by imposing a dress code for school dances?" Which group do you think favors a dress code and which opposes it? Explain.
- A study of reactions to different types of billboard advertising is to be carried out. Two different types of ads (call them Type I and Type II) for each product will be featured on numerous billboards. The organizer of the campaign is concerned that communities representing different economic strata will react differently to the ads. The three communities where billboards will be placed have been identified as Upper Middle, Middle, and Lower Middle. Four billboards are available in each of the three communities. Design a study to compare the effectiveness of the two types of advertising taking into account the communities involved.
- In 1976, Shere Hite published a book entitled The Hite Report on Female Sexuality. The conclusions reported in the book were based on 3000 returned surveys from some 100,000 sent out to, and distributed by, various women's groups. The results were that women were highly critical of men. In what way might the author's findings have been biased?
- You have 26 women available for a study: Annie, Betty, Clara, Darlene, Edie, Fay, Grace, Helen, Ina, Jane, Koko, Laura, Mary, Nancy, Ophelia, Patty, Quincy, Robin, Suzy, Tina, Ulla, Vivien, Wanda, Xena, Yolanda, and Zoe. The women need to be divided into four groups for the purpose of the study. Explain how you could use a table of random digits to make the needed assignments.
You decide to control for the possible confounding effect of the river by planting one of each type of strawberry in plots 1–5 and one of each type in plots 6–10 (that is, you block to control for the river). Then, within each block, you randomly assign one type of strawberry to each of the five plots within the block. What is the purpose of randomization in this situation?
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