Surveys and Samples

A retail company has 50 large stores located in different areas throughout a state. A researcher for the company believes that employee job satisfaction varies greatly from store to store. Which of the following sampling methods is most appropriate to estimate the proportion of all employees of the company who are satisfied with their job?

• Selecting one of the 50 stores at random and then surveying each employee at that store.

• Selecting 10 employees from each store at random and then surveying each employee selected.

• Surveying the 25 highest-paid employees and the 25 lowest-paid employees.

• Creating a website on which employees can express their opinions and then using the first 50 responses.

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Near the end of a US cable news show, the host invited viewers to respond to a poll on the show’s website that asked, “Do you support the new federal policy discussed during the show?” At the end of the show, the host reported that 28% responded “Yes,” and 70% responded “No.” Which of the following best explains why the results are unlikely to represent the sentiments of the population of the United States?

• The percentages do not add up to 100%, so any possible conclusions from the poll are invalid.

• Those who responded to the poll were not a random sample of the population of the United States.

• There were not 50% “Yes” responses and 50% “No” responses.

• The show did not allow viewers enough time to respond to the poll.

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For the finale of a TV show, viewers could use either social media or a text message to vote for their favorite of two contestants. The contestant receiving more than 50% of the vote won. An estimated 10% of the viewers voted, and 30% of the votes were cast on social media. Contestant 2 earned 70% of the votes cast using social media and 40% of the votes cast using a text message. Based on this information, which of the following is an accurate conclusion?

• If all viewers had voted, Contestant 2 would have won.

• Viewers voting by social media were likely to be younger than viewers voting by text message.

• If all viewers who voted had voted by social media instead of by text message, Contestant 2 would have won.

• Viewers voting by social media were more likely to prefer Contestant 2 than were viewers voting by text message.

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A market researcher selected 200 people at random from a group of people who indicated that they liked a certain book. The 200 people were shown a movie based on the book and then asked whether they liked or disliked the movie. Of those surveyed, 95% said they disliked the movie. Which of the following inferences can appropriately be drawn from this survey result?

• At least 95% of people who go see movies will dislike this movie.

• At least 95% of people who read books will dislike this movie.

• Most people who dislike this book will like this movie.

• Most people who like this book will dislike this movie.

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The members of a city council wanted to assess the opinions of all city residents about converting an open field into a dog park. The council surveyed a sample of 500 city residents who own dogs. The survey showed that the majority of those sampled were in favor of the dog park. Which of the following is true about the city council’s survey?

• It shows that the majority of city residents are in favor of the dog park

• The survey sample should have included more residents who are dog owners

• The survey sample should have consisted entirely of residents who do not own dogs.

• The survey sample is biased because it is not representative of all city residents.

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A polling agency recently surveyed 1,000 adults who were selected at random from a large city and asked each of the adults, “Are you satisfied with the quality of air in the city?” Of those surveyed, 78 percent responded that they were satisfied with the quality of air in the city. Based on the results of the survey, which of the following statements must be true?

i. Of all adults in the city, 78 percent are satisfied with the quality of air in the city.

ii. If another 1,000 adults selected at random from the city were surveyed, 78 percent of them would report they are satisfied with the quality of the air in the city.

iii. If 1,000 adults selected at random from a different city were surveyed, 78 percent of them would report they are satisfied with the quality of air in the city.

• None

• ii only

• i and ii only

• i and iii only

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In order to determine if treatment X is successful in improving eyesight, a research study was conducted. From a large population of people with poor eyesight, 300 participants were selected at random. Half of the participants were randomly assigned to receive treatment X, and the other half did not receive treatment X. The resulting data showed that participants who received treatment X had significantly improved eyesight as compared to those who did not receive treatment X. Based on the design and results of the study, which of the following is an appropriate conclusion?

• Treatment X is likely to improve the eyesight of people who have poor eyesight.

• Treatment X improves eyesight better than all other available treatments.

• Treatment X will improve the eyesight of anyone who takes it.

• Treatment X will cause a substantial improvement in eyesight.

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