AP Free Reponse Problems

Block Design WorksheetExperimental Design

1. Some health care professionals recommend the use of melatonin to promote better sleep patterns. To test this idea the manufacturer has 100 of its employees fill out a questionnaire about their sleeping patterns, once at the beginning of the study and then again after taking a 3-milligram melatonin capsule every night at bedtime for a week. Comment on the design of this experiment.

This is really an observational study. They aren’t clear about what they are measuring. They only state that they are given a questionnaire about their sleep patterns. They tried to do a completely randomized design…but didn’t quite make it.

2. A new weight-loss supplement is to be tested at three different levels (once, twice, and three times a day). The supplement is believed to work differently in women than in men. Design an experiment, including a control group and blocking, for 80 overweight volunteers, half of whom are men. Explain carefully how you will use randomization.

This is a randomized block experiment. The 80 overweight volunteers will be blocked first by gender since gender may create more variation in the data. I will then place the 40 men’s names in a hat and draw 10 without replacement. They will take the supplement once a day. I will draw another 10 names, without replacement and these men will take the supplement twice a day. I will draw another 10 names without replacement and these men will take the supplement three times a day. The remaining 10 men will not take a supplement. This will be the control group. We will measure the amount of weight lost. Repeat this process for the women.

3. Two studies are run to measure the health benefits of long-time use of daily high doses of vitamin C. Researchers in the first study send a questionnaire to all 50,000 subscribers to a health magazine, asking whether they have taken large doses of vitamin C for at least a 2-year period and what the perceive to be the health benefits, if any. The response rate is 80%. The 10,000 people who did not respond to the first mailing receive follow-up telephone calls, and eventually responses are registered from 98% of the magazine subscribers. Researchers in a second study take a group of 200 volunteers and randomly select 100 to receive high doses of vitamin C while the others receive a similar-looking, similar-tasting placebo. The volunteers are not told whether they are receiving the vitamin, but their doctors know and are asked to note health changes during a 2-year period. Comment on the designs of the two studies.

The first study is an observational study and you cannot make any cause/effect statements from it. It does have selection bias since they only sample from subscribers of the health magazine which is probably people who are already fit, thus many unfit people are left out of the study.

The second study is a completely randomized experiment with two treatments, the ones who take vitamin C and the ones who get the placebo. The placebo is like a control group, but this will take care of any variation that may result from the placebo effect. Since the patient does not know what medication they are receiving, but the doctor does know, then this is a single blind experiment.

4. A new vegetable fertilizer is to be tested at two different levels (regular concentration and double concentration). Design an experiment, including a control, for 30 test plots, half of which are in shade. Explain carefully how you will use randomization.

This is a randomized block experiment. There are 2 blocks. The plots of land are already either in the shade or in the sun. The amount of sunlight can affect the growth of the plant, thus we block based on this characteristic in order to reduce the variation. Label the 15 plots in the shade with a unique number from 1 to 15 and use a random number generator on the calculator to randomly generate five numbers without replacement. These five plots will get regular concentrated fertilizer. Then randomly generate five more numbers without replacement. These plots will get the double concentrated fertilizer. The five remaining plots will be the control group and so they will not get any fertilizer. We will measure the growth of the vegetable. Repeat this process with the plots of land that are in the sun.