Probability & Statistics Honors Unit Test #5

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Bayer HealthCare LLC produces low-dose aspirin pills designed to contain 81 mg of aspirin. Because each pill contains other ingredients, including corn starch, talc, and propylene glycol, it is difficult to check whether manufactured pills contain 81 mg of aspirin. A quality control plan is to select every 1000th pill, which is then tested for the correct amount of aspirin.

Use this information for questions 1 – 3.

 1 What is the population in this study? (4)

All low-dose aspirin pills produced by this company.

 2 To what group can the results of this study be generalized? (4)

All low-dose aspirin pills produced by this company.

 3 What sampling method is being used in this example? (2)

Systematic

 4 The Milgram Research Company wants to study reactions to stress, so it administers surveys in which the person asking the questions pretends to become very angry with the survey subject. At one point, the surveyor screams at the subject and asks how anyone could have such “stupid” opinions. The interviewee’s reaction is recorded. Is this an example of an observational study or an experiment? (3)

Experiment—something is changed/a treatment is applied. This isn’t a good experiment, since there is no comparison group mentioned, but they are doing more than simply observing.

 5 A State Senator randomly selects a group of parents whose children attend public schools to receive a survey about using vouchers for private education. What type of bias does this sample exhibit? (3)

Undercoverage. The Senator might want to ask parents of children who attend private schools as well!

A researcher wants to know if adding meditation to medication can better control patients’ high blood pressure. 64 patients with high blood pressure that have never practiced meditation nor taken medication for their high blood pressure have been recruited for this study. The doctor randomly assigns half of the patients to practice meditation while taking medication, and the other half to only take medication. After six months, the change in each patient’s blood pressure is measured.

 6 What are the experimental units in this experiment? (2)

The 64 patients with high blood pressure

 7 What is/are the explanatory variable/s in this experiment? (3)

Blood pressure control method

 8 What are the treatments in this experiment? (3)

[1] meditation and medication, or [2] medication only

 9 What is the response variable in this experiment? (2)

Change in blood pressure

 10 Is a placebo being used in this experiment? (2)

No. Nothing is being done that should have no effect, or a known effect.

 11 Can this experiment be made double-blind? (4)

No. The patients will surely know that they are practicing meditation!

 12 Why is it important to randomly assign patients to the treatment groups? (4)

Random assignment helps to avoid confounding with extraneous variables. If we didn’t randomly assign, then we might assign patients who had higher blood pressures to the meditation group, and it might then look like meditation didn’t help even if it worked just as well as medication.

 13 Lisinipril is a drug designed to lower blood pressure. 100 volunteers have been recruited to measure its effects. 50 are randomly selected to receive this drug; the other 50 will receive the currently recommended blood pressure medication. Each volunteer will have their blood pressure measured before and after the study, so that the difference (change) due to the drug can be measured. What type of experimental design is being described? (2)

Completely randomized design

 14 In order to test the durability of a new waterproofing method, the quality control department of a shoe manufacturer recruited fifty people in a city where it rains frequently to wear their shoes for a month. Half of the volunteers received a pair of shoes where the left shoe was treated with the new waterproofing method and the right shoe was treated with the old method (the treatments were reversed for the rest of the volunteers). They wore these shoes for two weeks, then returned them and exchanged them for another pair (where the show that was waterproofed with the new method was opposite of the original one). Each volunteers wore these shoes for two weeks, then returned the shoes. All of the shoes were evaluated for water damage. What type of experimental design is being described? (2)

Matched pairs

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