AP STATS CHAPTER 4

The Hemlock Woolly Adelgid is an insect that has accidentally been released in Eastern U.S.

forests from Asia. Since it has no natural enemies in the U.S., it is spreading rapidly. A forester studying the abundance of the insect in southern Vermont wants to determine if it has spread that far north. He randomly selects 200 hemlock trees in a large Vermont forest and finds that 46 of them show signs of damage from this insect. To which of the following groups of trees would it be

appropriate to generalize the results of the study?

• All hemlock trees in southern Vermont

• All trees in southern Vermont

• The 200 hemlock trees that were randomly selected

• All hemlock trees in the U.S.

• All hemlock trees in the forest from which the 200 trees were selected

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CCSS.7.SP.A.1

CCSS.HSS.IC.A.1

Which of the following is a method for improving the accuracy of a sample?

• use no more thatn 3 or words in a question

• when possible, avoid the use of human interviewers, relying on computerized dialing instead

• use larger sample sizes

• use smaller sample sizes

• ask only questions for which the reponses are quantitative variables

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CCSS.HSS.IC.B.4

A sample of student opinion at a Big Ten University selects an SRS of 200 of the 30,000 undergraduate students and a another SRS of 100 of the 5,000 graduates. What is the term for this kind of sample?

• Simple random sample

• Simple random sample with blocking

• Stratified random sample

• Cluster random sample

• Systematic random sample

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CCSS.HSS.IC.B.3

For a certain experiment you have 8 subjects, of which 4 are female and 4 are male. The name of the subjects are listed below:

Males: Atwater, Bacon, Chu, Diaz.

Females: Johnson, King, Liu, Moore

There are to be two treatment groups, A and B. If a randomized block design is used, with the subjects blocked by their gender, which of the following is not a possible group of subjects for treatment group A?

• Atwater, Chu, King, Liu

• Bacon, Chu, Liu, Moore

• Atwater, Diaz, Liu, King

• Atwater, Bacon, Chu, Johnson

• Atwater, Bacon, Johnson, King

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CCSS.HSS.IC.B.3

An Illinois school district wants to compare the effectiveness of a standard AP Statistics curriculum

and a new “hands-on” AP Statistics curriculum. Two experienced teachers, Mrs. Militello and Mrs. Grozik, each teach one class with the standard curriculum and one with the new approach. Students are assigned at random to these four classes. At the end of the year, all students take the AP Statistics exam. Which of the following are the experimental units in this experiment?

• Mrs Militello and Mrs Grozik

• The two AP Statistics curriculum

• The students in the four classes

• The students taking the AP exam in IL

• The four classes

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CCSS.HSS.IC.B.3

CCSS.HSS.IC.B.5

An Illinois school district wants to compare the effectiveness of a standard AP Statistics curriculum

and a new “hands-on” AP Statistics curriculum. Two experienced teachers, Mrs. Militello and Mrs. Grozik, each teach one class with the standard curriculum and one with the new approach. Students are assigned at random to these four classes. At the end of the year, all students take the AP Statistics exam. The AP Stats experiment in the previous question has

• on factor: the type of AP Stats curriculum a student is assigned to

• two factors: the type of AP Stats curriculum and the teacher a student is assigned to

• two factors: the standard curriculum and the new hands-on approach

• three factors: the type of AP Statistics curriculum, the teacher, and the class a student is assigned to

• three factors: the standard curriculum, the hands-on approach, and the teacher a student is assigned to

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CCSS.HSS.IC.B.3

A materials engineer wishes to compare the durability of two different types of paving material. She has 40 different one-mile stretches of interstate highway that she’s been authorized to repave for this study. She decides to carry out a matched pairs experiment. Which of the following is the

best way for her to carry out the randomization for this study?

• Use a table of random digits to divide the 40 roadways into 20 pairs and then, for each pair, flip a coin to decide which pavement to use on which member of the pair.

• Subjectively divide the 40 roadways into 20 pairs (making the roadways within each pair as different as possible) and then, for each pair, flip a coin to decide which pavement to use on

  which member of the pair.

• Use a table of random digits to divide the 40 roadways into two groups of twenty, and then use the table of random digits a second time to decide which pavement to use on which group.

• Let each of the 40 roadways act as its own pair, dividing each roadway into the first half-mile and the second half-mile. Flip a coin for each of the 40 roadways to decide which half-mile

  gets which pavement.

• Let each of the 40 roadways act as its own pair, dividing each roadway into the first half-mile and the second half-mile. Flip a coin once to decide which pavement is put on the first half-mile

  of all the roadways.

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CCSS.HSS.IC.B.3

A program that was intended to cure a person’s fear of spiders was offered at a local zoo. Volunteers with a fear of spiders participated in the program, which included holding a spider for 15 minutes. One month after they completed the program, the participants were contacted and surveyed about the program. Over 90 percent of the participants claimed they were cured of their fear of spiders. Based on the description of the program, which of the following statements is true?

• Because over 90% of the participants claimed to be cured, the results prove that holding a spider will cure a person’s fear of spiders.

• Because over 90% of the participants claimed to be cured, the results can be generalized to the population of all people who have a fear of spiders.

• Because the participants were volunteers, the study is a census of all people in the local area who have a fear of spiders.

• Because the participants were self-selected, a person’s desire to be cured could be a confounding variable.

• Because participants held a spider for 15 minutes, the study is an experiment and the results can be generalized to the population of all people who have a fear of spiders.

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CCSS.HSS.IC.B.3

The quality-control manager of a large factory is concerned about the number of defective items produced by workers. Thirty workers at the factory agree to participate in a study of three different incentive plans to help reduce the number of defective items produced. The plans will be randomly assigned to the workers so that 10 workers received each plan. The reduction in the number of defective items produced by each worker will be recorded two weeks after the plans are implemented.

Which of the following best describes why a completely randomized design is an appropriate design to use in this situation?

• There is no blocking variable, and incentive plans will be randomly assigned to the workers.

• There is no blocking variable, and the workers were selected at random.

• Each incentive plan is a block, and a completely randomized design is not blocked.

• Each plan will be randomly assigned to 10 pairs of workers who share a similar characteristic.

• The number of workers participating in the study was greater than or equal to 30.

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CCSS.HSS.IC.B.3

CCSS.HSS.IC.B.5

The director of a community recreation center conducted a six-week study to examine the effects of four types of exercise—strength training, flexibility training, aerobics, and jogging—on maximal oxygen consumption. From the 40

members who participated, the director randomly assigned 10 members to each exercise type. Maximal oxygen consumption was measured for each member at the beginning of the study and again at the end of the six weeks. The director examined the change in maximal oxygen consumption for each member. Which of the following statements is a correct description of a feature of the study?

• The study has replication because there are four types of exercise.

• The study has replication because it was conducted over a six-week period.

• The response variable is the type of exercise with the greatest change in maximal oxygen consumption.

• The treatments in the study are strength training, flexibility training, aerobics, and jogging.

• The experimental units are the four different types of exercise.

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