A psychologist designed and conducted a study to determine whether playing a certain educational game increases middle school students’ accuracy in adding fractions. For the study, the psychologist chose a random sample of 35 students from all of the students at one of the middle schools in a large city. The psychologist found that students who played the game improved accuracy when adding fractions. What is the largest group to which the study results can be generalized?

A) The 35 students in the sample

B) All students at the school

C) All students at the middle school from which the sample was drawn

D) All students in the city

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?

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

B) Those who responded to the poll were not a random sample of the population of the United States

C) There were not 50% “Yes” responses and 50% “No” responses

D) The show did not allow viewers enough time to respond to the poll

A bag containing 10,000 beads of assorted colors is purchased from a craft store. To estimate the percent of red beads in the bag, a sample of beads is selected at random. The percent of red beads in the bag was estimated to be 15%, with an associated margin of error of 2%. If r is the actual number of red beads in the bag, which of the following is most plausible?

A) r > 1,700

B) 1,300 < r < 1,700

C) 200 < r < 1,500

D) r < 1,500

In State X, Mr. Camp’s eighth-grade class consisting of 26 students was surveyed and 34.6 percent of the students reported that they had at least two siblings. The average eighth‑grade class size in the state is 26. If the students in Mr. Camp’s class are representative of students in the state’s eighth-grade classes and there are 1,800 eighth-grade classes in the state, which of the following best estimates the number of eighth‑grade students in the state who have fewer than two siblings?

A) 16,200

B) 23,400

C) 30,600

D) 46,800

The results of two random samples of votes for a proposition are shown above. The samples were selected from the same population, and the margins of error were calculated using the same method. Which of the following is the most appropriate reason that the margin of error for sample A is greater than the margin of error for sample B?

A) Sample A had a smaller number of votes that could not be recorded.

B) Sample A had a higher percentage of favorable responses.

C) Sample A had a larger sample size.

D) Sample A is smaller.