Statistical Inference

A teacher wants to know if students at a particular high school are in favor of a new school policy that allows students to carry cell phones during school hours. The teacher is not able to ask the opinion of every student at the school, so she needs to select an appropriate sample of the students. The best way to do this is for the teacher to ask

• Students at a randomly selected table from all of those in the lunch room.
• Students selected by the principal.
• Students she can select and talk to between classes.
• Students randomly selected from a list of all students at the school.

A tenth grade class of twenty-seven students wants to estimate the proportion of eligible voters in their school district who intend to vote in the upcoming school board election. They decide to base their estimate on 270 eligible voters. Which of the following plans would allow the class to generalize from the sample to the population of all eligible voters?

• Mail surveys to 270 randomly selected eligible voters and follow-up with those who do not respond.
• Survey 270 people visiting a local grocery store on the Saturday before the election.
• Mail surveys to all eligible voters and take the first 270 who respond.
• Have each of the 27 students randomly select 10 neighbors to participate in the survey.

A student wants to estimate the mean number of books that have been read by all students at his school over the summer. On Monday morning, he will survey the first 35 students who enter the library. Is this the best way to select a sample for this purpose?

• No. The student should survey students entering the library on more than one day of the week.
• No. The student should take a random sample of students entering the library instead.
• No. The student should take a random sample of students from all students, not just those entering the library.
• Yes. Selecting a sample in this way will not introduce the possibility of bias.

The President of a large university with 30,000 students wants to investigate student support for an increase in tuition (the cost to enroll in classes). The President requests a sample of 200 students. Which of the following methods of sample selection would be best?

• Select 200 students at random from those in the campus bookstore on the first day of class.
• Select 50 students at random from the list of the 10,000 students living in dorms on campus.
• Select 50 students at random from each of the first four football games of the season.
• Select 200 students at random from the list of students currently enrolled at the university.

A study was conducted to investigate whether washing with soap and water or using hand sanitizer removes more bacteria from a person's hands. Volunteers were recruited from a high school and randomly assigned to a group that washed their hands with soap and water or to a group that used hand sanitizer. When they were finished, each volunteer pressed his or her hands into specially prepared petri dishes. After several days, the number of bacteria colonies was counted on each petri dish. Which of the following statements best describes the random assignment in this study?

• The random assignment was important so that these results could be applied to all high school students.
• The random assignment was important because it tends to create groups that are similar with respect to other variables that might affect bacteria growth.
• Including random assignment was incorrect because students should be divided into the two groups based on their usual method of cleaning their hands.
• The random assignment was unnecessary because using volunteers makes the study worthless.

Lee wants to answer the question, “What proportion of sophomores at my high school plan to take a foreign language class during the next school year?” Which of the following methods would best allow Lee to answer his question?

• Randomly select 40 sophomores from the high school and ask them if they intend to take a foreign language course next year.
• Randomly select 50 students from the high school and ask them if they intend to take a foreign language class next year.
• Randomly select half of the foreign language teachers in the high school and ask them how many students are taking their classes this year.
• Randomly select half of the sophomores taking Spanish this year and ask them if they intend to take Spanish next year.

Rebecca wants to know how many books students in her school read over summer vacation. She attends a large school, and doesn’t have time to ask every student. Which of the following would best allow her to make generalizations about all students in her school?

• Select all of the students in her English class
• Select the first 40 students that she sees after school
• Select 40 students from her school at random
• Select 40 of the students in the library at random