Statistics AP (Chapter 4)

You want to take a simple random sample (SRS) of 50 of the 816 students who live in a dormitory on campus. You label the students 001 to 816 in alphabetical order. In the table of random digits, you read the entries (shown in the image).

The first three students in your sample have labels

• 955, 929, 400

• 400, 769, 769

• 559, 294, 007

• 929, 400, 769

• 400, 769, 335

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In order to assess the opinion of students at the University of Minnesota on campus snow removal, a reporter for the student newspaper interviews the first 12 students he meets who are willing to express their opinion. The method of sampling used is

• a census

• a stratified random sample

• a voluntary sample

• a convenience sample

• a simple random sample

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The transportation department of a large city wants to estimate the proportion of residents who would use a system of aerial gondolas to commute to work. The gondolas would be part of the city’s effort to relieve traffic congestion. The department asked a random sample of residents whether they would use the gondolas. The residents could respond with yes, no, or maybe. Which of the following is the best description of the method for data collection used by the department?

• A census

• A sample survey

• An experiment with a completely randomized design

• An experiment with a randomized block design

• An experiment with a matched-pairs design

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A television station is interested in predicting whether voters in its viewing area are in favor of offshore drilling. It asks its viewers to phone in and indicate whether they support/are in favor of or are opposed to this practice. Of the 2241 viewers who phoned in, 1574 (70%) were opposed to offshore drilling. The viewers who phoned in are

• a voluntary response sample

• a convenience sample

• a simple random sample

• a completely randomized design

• a confounding variable

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In designing an experiment, blocking is used

• To reduce bias.

• To reduce variation.

• As a substitute for a control group.

• As a first step in randomization.

• To control the level of the experiment.

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CCSS.HSS.IC.B.3

Ann Landers, who wrote a daily advice column appearing in newspapers across the country, once asked her readers, “If you had to do it over again, would you have children?” Of the more than 10,000 readers who responded, 70% said no. What does this show?

• The survey is meaningless because of voluntary response bias.

• No meaningful conclusion is possible without knowing something more about the characteristics of her readers.

• The survey would have been more meaningful if she had picked a random sample of the 10,000 readers who responded.

• The survey would have been more meaningful if she had used a control group.

• This was a legitimate sample, randomly drawn from her readers and of sufficient size to allow the conclusion that most of her readers who are parents would have second thoughts about having children.

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A marine biologist wants to estimate the mean size of the barnacle Semibalanus balnoides on a stretch of rocky shoreline. To do so, he randomly selected twenty 10-cm. square plots and measured the size of every barnacle in each plot. This is an example of

• convenience sampling.

• cluster sampling.

• stratified random sampling.

• simple random sampling.

• multistage sampling.

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CCSS.HSS.IC.B.3

Are dogs better at tracking the movements of brightly colored objects? Fifteen experienced “disk dogs” who have been trained to catch flying disks in mid-air are given the chance to catch a bright red disk or a plain white disk. Each disk is thrown 10 times for each dog, with the sequence of disks (red or white) determined randomly. The proportion of red disks caught to the proportion of white disks caught is compared for each dog. This is an example of a

• Simple random sample

• Stratified random sample.

• Completely randomized design.

• Matched pairs design.

• A block design, but not a matched pairs design.

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CCSS.HSS.IC.B.3

A compact disc (CD) manufacturer wanted to determine which of two different cover designs for a newly released CD will generate more sales. The manufacturer chose 70 stores to sell the CD. Thirty-five of these stores were randomly assigned to sell CDs with one of the cover designs and the other 35 were assigned to sell the CDs with the other cover design. The manufacturer recorded the number of CDs sold at each of the stores and found a significant difference between the mean number of CDs sold for the two cover designs. Which of the following gives the conclusion that should be made based on the results and provides the best explanation for the conclusion?

• It is NOT reasonable to conclude that the difference in sales was caused by the different cover designs because this was not an experiment.

• It is NOT reasonable to conclude that the difference in sales was caused by the different cover designs because there was no control group for comparison.

• It is NOT reasonable to conclude that the difference in sales was caused by the different cover designs because the 70 stores were not randomly chosen.

• It is reasonable to conclude that the difference in sales was caused by the different cover designs because the cover designs were randomly assigned to stores.

• It is reasonable to conclude that the difference in sales was caused by the different cover designs because the sample size was large.

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Which of the following distinguishes an observational study from a randomized experiment?

• In an observational study volunteers are always used, whereas in a randomized experiment a random sample is always taken from the population.

• In an observational study a random sample is always taken from the population, whereas in a randomized experiment volunteers are always used.

• In an observational study treatments are not randomly assigned, whereas in a randomized experiment treatments are randomly assigned.

• In an observational study a control group is never used, whereas in a randomized experiment a control group is always used.

• An observational study can be double-blind, whereas a randomized experiment can only be single-blind because the experimenter determines who is randomly assigned to each treatment.

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