Probability & Statistics Honors Unit Test #5

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A furniture maker buys hardwood in large batches. The supplier is supposed to dry the wood before shipping (to keep its size and shape). The furniture maker chooses five pieces of wood from each of three batches and tests their moisture content.

Use this information for the first three questions.

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

All of the wood in the three batches.

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

All of the wood in the three batches.

 3 What sampling method has been described in this scenario? (2)

Stratified random sample

 4 Researchers at Stanford University conducted a study in a campus cafeteria. Each day for an entire semester, the cafeteria served an identical vegetable dish that was randomly labeled one of four ways: Basic, Healthy/Restrictive, Healthy/Positive, or Indulgent. The researchers covertly noted how many students chose the vegetable dish each day, and how much the students served themselves. Is this an example of an observational study or an experiment? Why? (3)

An experiment—something was changed (the food label).

 5 A research group called random phone numbers between 8am and 5pm and asked respondents if they were a stay-at-home parent with children. What type of bias is present in this sampling technique? (3)

Undercoverage (this won’t call anyone who works away from home during the day).

Researchers at Rutgers University tested the “five second rule.” The researchers tested four different foods and four different contact times. In each case, they then took swabs and measured the amount of bacteria present on the food.

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

Single items of food

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

Food type and contact time

 8 How many treatments are there in this experiment? (3)

16

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

Amount of bacteria

 10 Was a placebo used in this experiment? (3)

No—there is no treatment with either no effect, or a known effect.

 11 Why was it important for the researchers to randomly assign the experimental units to each of the treatments? (4)

The random assignment will help deal with unknown variables that might have some effect on the amount of bacteria (i.e., lurking variables).

 12 A researcher wants to test the effect of three teaching methods on student performance. The researcher selects students randomly from those registered for a particular course. The researcher groups the students by IQ levels (low, average, high). Within each group, each student is randomly assigned to a different teaching method. What type of experimental design is being described? (2)

Randomized block

 13 What is the most effective shark repellant? Five different products were tested. Six identical surfboards were obtained. Five were randomly chosen to have one of the shark repellants applied (the sixth had no repellant applied). All six boards were tested in similar water conditions by attaching raw tuna on a line dragging behind the board. In each trial, it was noted whether or not a shark attempted to eat the tuna. What type of experimental design is being described? (2)

Completely randomized

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