Chapter 4 Review - Multiple Choice

The primary advantage of controlled experiments over observational studies is that:

• observational studies cannot be generalized to a larger population.

• observational studies do not have explanatory variables.

• experiments are less time-consuming to conduct.

• experiments provide stronger evidence of cause-and-effect relationships.

Answer explanation

The primary advantage of controlled experiments is that they allow researchers to manipulate variables and establish cause-and-effect relationships, providing stronger evidence than observational studies, which can only suggest correlations.

A school principal wants to gather student opinions on a new lunch menu. To do this, she uses a random number generator to select 15 students from the entire student body to complete a survey about the menu changes. The 15 students selected are:

• the population.

• a voluntary response sample.

• a convenience sample.

• a simple random sample of the student body.

Answer explanation

The principal used a random number generator to select students, ensuring each had an equal chance of being chosen. This method defines a simple random sample, representing the student body effectively.

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Some news organizations maintain a database of customers who have volunteered to share their opinions on a variety of issues. Suppose that one of these databases includes 9000 registered voters in California. To measure the amount of support for a controversial ballot issue, 1000 registered voters in California are randomly selected from the database and asked their opinion. Which of the following is the largest population to which the results of this survey should be generalized?

• The 1000 people in the sample

• The 9000 registered voters from California in the database

• All registered voters nationwide

• All California residents

Answer explanation

The results should be generalized to the 9000 registered voters in the database, as they represent the larger group from which the sample was drawn. The sample of 1000 is too small, and the other options are not relevant.

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Some studies of the relationship between car color and frequency of accidents have found that red cars are more likely to be in accidents than black cars, despite how visible they are. Some experts warn that we should not conclude red cars are less safe than black cars because of possible confounding. Which of the following best describes what this means?

• There are too many variables involved in traffic accidents to isolate the effect of car color.

• The accidents used in the study might not be a random sample of all accidents.

• It is not possible to separate the effect of car color from the type of people who choose to drive red cars.

• It can be hard to determine if red cars or black cars are more visible on modern highways.

Answer explanation

The correct choice highlights that the relationship between car color and accidents may be influenced by the characteristics of drivers who choose red cars, making it difficult to isolate the effect of color alone.

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Which one of the following is a valid statistical question?

• How tall is the Empire State Building?

• How many points did LeBron James score in the 2018 NBA playoffs?

• When you call your cell-phone provider’s customer service number, how long will you typically be on hold?

• How much money did Ivan’s family spend on groceries last month?

Answer explanation

The correct choice is about typical hold times, which can vary and be analyzed statistically. The other options seek specific values, not statistical data that can be collected from a population.

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What is the most important reason for random assignment of treatments in an experiment?

• To ensure that no specific groups in the population are systematically left out of the experiment.

• To minimize bias in selecting subjects for the experiment.

• To remove the necessity of blinding in an experiment.

• To create groups that are roughly equivalent before treatments are applied.

Answer explanation

The most important reason for random assignment is to create groups that are roughly equivalent before treatments are applied, which helps ensure that the results are due to the treatments rather than pre-existing differences.

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A local environmental group wants to measure public support for a proposed city wide ban on single-use plastic bags. They plan to conduct a survey to gather unbiased results. Which of the following methods would produce the most reliable results?

• Call a random selection of phone numbers nationwide and ask respondents if they support the citywide ban.

• Select a random sample of registered voters in the city, call them, and ask whether they support the plastic bag ban.

• Set up a booth at a weekend farmer’s market and ask shoppers to take a survey about their opinions on the plastic bag ban.

• Mail surveys to all city residents and instruct them to return the survey if they wish to share their opinion.

Answer explanation

Selecting a random sample of registered voters in the city ensures that the survey targets the relevant population directly affected by the ban, leading to more reliable and representative results.

A sportswriter wants to know how strongly Albuquerque residents support the local minor league baseball team, the Isotopes. She stands outside the stadium before a game and interviews the first 20 people who enter the stadium, asking them to rate their enthusiasm for the team on a 1 (lowest) to 5 (highest) scale. Which of the following best describes the results of this survey?

• Because this is a random sample, there will be some sampling variability, but we can expect it to produce quite accurate results.

• This is a random sample, but the size of the sample is too small to produce reliable results.

• This is a voluntary response sample and is likely to underestimate support for the team.

• This is a convenience sample and is likely to overestimate the level of support for the team.

Answer explanation

The survey is a convenience sample since the writer only interviewed people entering the stadium, likely leading to an overestimation of support for the Isotopes, as these individuals are already fans.

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A local news agency conducted a survey about unemployment by randomly dialing phone numbers until it had gathered responses from 1000 adults in the state. In the survey, 19% of those who responded said they were not currently employed. In reality, only 6% of the adults in the state were not currently employed at the time of the survey. Which of the following best explains the difference in the two percentages?

• The difference is due to sampling variability. We shouldn’t expect the results of a random sample to match the truth about the population every time.

• The difference is due to response bias. Adults who are employed are likely to lie and say that they are unemployed.

• The difference is due to undercoverage. The survey included only adults and did not include teenagers who are eligible to work.

• The difference is due to nonresponse. Adults who are employed are less likely to be available for the sample than adults who are unemployed.

Answer explanation

The difference is due to nonresponse. Employed adults may be less available for the survey, leading to an overrepresentation of unemployed respondents, which skews the results.

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A new headache remedy was given to a group of 25 subjects who had headaches. Four hours after taking the new remedy, 20 of the subjects reported that their headaches had disappeared. From this information, you conclude…

• that the remedy is effective for the treatment of headaches.

• nothing because the sample size is too small.

• nothing because there is no control group for comparison.

• that the new treatment is better than aspirin.

Answer explanation

The conclusion is that nothing can be determined about the remedy's effectiveness because there is no control group for comparison. Without a control group, we cannot attribute the headache relief solely to the new remedy.