Conclusions from Studies

A community center offers a Spanish course.  This year, all students in the course were offered additional audio lessons they could take at home.  The students who took these additional audio lessons did better in the course than students who didn’t take the additional audio lessons.  Based on these results, which of the following is the most appropriate conclusion?

• Taking additional audio lessons will cause an improvement for any student who takes any foreign language course.

• Taking additional audio lessons will cause an improvement for any student who take a Spanish course.

• Taking additional audio lessons was the cause of the improvement for the students at the community center who took the Spanish course.

• No conclusion about cause and effect can be made regarding students at the community center who took the additional audio lessons at home and their performance in the Spanish course.

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.

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.

A study was done on the weights of different types of fish in a pond. A random sample of fish were caught and marked in order to ensure that none were weighed more than once. The sample contained 150 largemouth bass, of which 30% weighed more than 2 pounds. Which of the following conclusions is best supported by the sample data?

• The majority of all fish in the pond weigh less than 2 pounds.

• The average weight of all fish in the pond is approximately 2 pounds.

• Approximately 30% of all fish in the pond weigh more than 2 pounds.

• Approximately 30% of all largemouth bass in the pond weigh more than 2 pounds.

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.

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 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

To determine the mean number of children per household in a community, Tabitha surveyed 20 families at a playground. For the 20 families surveyed, the mean number of children per household was 2.4. Which of the following statements must be true?

• The mean number of children per household in the community is 2.4.

• A determination about the mean number of children per household in the community should not be made because the sample size is too small.

• The sampling method is flawed and may produce a biased estimate of the mean number of children per household in the community.

• The sampling method is not flawed and is likely to produce an unbiased estimate of the mean number of children per household in the community.

A sample of 40 fourth-grade students was selected at random from a certain school. The 40 students completed a survey about the morning announcements, and 32 thought the announcements were helpful. Which of the following is the largest population to which the results of the survey can be applied?

• The 40 students who were surveyed.

• All fourth-grade students at the school.

• All students at the school.

• All fourth-grade students in the county in which the school is located.