5.1 Review

In a certain school, students can choose whether to eat in the school’s cafeteria. A reporter working for the school’s newspaper polled students on their reactions to changes in the menu at the cafeteria. For each student leaving the cafeteria in one 30-minute time period, the reporter used a coin to determine whether to stop the student and ask how he or she felt about the new menu. In the reporter’s article it was stated that a random sample of the students showed that 89 percent of the school’s student population was happy with the new menu. Which of the following statements is true?

• Because each student leaving the cafeteria was randomly selected and could choose to answer or not, this is a random sample of the student population, and the 89% is an accurate measurement of the school population’s view of the new menu.

• Because students self-selected whether to eat in the cafeteria, the sampling method might be biased and the sample might not be representative of all students in the school.

• The survey would have been more effective if the reporter had collected the data in one 15-minute time period rather than in one 30-minute time period.

• The survey would have been more effective if students who cared about the food could have called the reporter to tell how they felt about the new menu, so that only students with opinions on the subject would have been surveyed.

• Because no treatment was imposed on the students eating in the cafeteria, one cannot make any conclusions about the new menu.

A bank surveyed all of its 60 employees to determine the proportion who participate in volunteer activities. Which of the following statements is true?

• The bank should not use the data from this survey because this is an observational study.

• The bank can use the result of this survey to prove that working for the bank causes employees to participate in volunteer activities.

• The bank did not select a random sample of employees, so the survey will not provide the bank with useful information.

• The bank would have to use the survey data to construct a confidence interval in order to estimate the proportion of employees who participate in volunteer activities.

• The bank does not need to use an inference procedure to determine the proportion of employees who participate in volunteer activities because the survey was a census of all employees.

In the design of a survey, which of the following best explains how to minimize response bias?

• Increase the sample size.

• Decrease the sample size.

• Randomly select the sample.

• Increase the number of questions in the survey.

• Carefully word and field-test survey questions.

A large simple random sample of people aged nineteen to thirty living in the state of Colorado was surveyed to determine which of two MP3 players just developed by a new company was preferred. To which of the following populations can the results of this survey be safely generalized?

• Only people aged nineteen to thirty living in the state of Colorado who were in this survey

• Only people aged nineteen to thirty living in the state of Colorado

• All people living in the state of Colorado

• Only people aged nineteen to thirty living in the United States

• All people living in the United States

A certain county school district has 15 high schools. The high school seniors’ plans after graduation in each school vary greatly from one school to the next. The county superintendent will select a sample of high school seniors from the district to survey about their plans after graduation. The superintendent will use a cluster sample with the high schools as clusters. A random sample of 5 high schools will be selected, and all seniors at those high schools will complete the survey. What is one disadvantage to selecting a cluster sample to investigate the superintendent’s goal?

• Cluster sampling is usually very expensive to implement and could cost the district too much money.

• Because every senior in the selected clusters will complete the survey, the sample will be too large to yield accurate results.

• The schools in the cluster sample might not be representative of the population of seniors.

• There could be seniors absent from school on the day the survey is given, which could affect the results.

• There is no disadvantage to using a cluster sample.

A researcher selects a simple random sample of 1,200 women who are students at Midwestern colleges in the United States to use for an observational study. Which of the following describes the population to which it would be most reasonable to generalize the results?

• All students in the United States

• All college students in the United States

• All women who are students in the United States

• All students at Midwestern colleges in the United States

• All women who are students at Midwestern colleges in the United States

A school nutritionist was interested in how students at a certain school would feel after taking a nutritional supplement. The nutritionist selected a random sample of twenty students from the school to participate in the study. Participants were asked to keep a journal on how well they felt after taking the supplement each day. What possible source of bias is present in the method of data collection?

• Bias from a sampling method that only uses volunteers

• Undercoverage bias

• Nonresponse bias

• Response bias where responses are self-reported

• Response bias where the question wording is leading or confusing

At a certain clothing store, the clothes are displayed on racks. The clothes on each rack have similar prices, but the prices among the racks are very different. To estimate the typical price of a single piece of clothing, a consumer will randomly select four pieces of clothing from each rack. What type of sample is the consumer selecting?

• A census

• A cluster sample

• A simple random sample

• A stratified random sample

• A systematic random sample

A polling firm is interested in surveying a representative sample of registered voters in the United States. The firm has automated its sampling so that random phone numbers within the United States are called. Each time a number is called, the procedure below is followed.

• If there is no response or if an answering machine is reached, another number is automatically called.

• If a person answers, a survey worker verifies that the person is at least 18 years of age.

• If the person is not at least 18 years of age, no response is recorded, and another number is called.

• If the person is at least 18 years of age, that person is surveyed.

Some people claim the procedure being used does not permit the results to be extended to all registered voters. Which of the following is NOT a legitimate concern about the procedure being used?

• Registered voters with children under the age of 18 years may be underrepresented in the sample.

• Registered voters with unlisted telephone numbers may be underrepresented in the sample.

• Registered voters who have more than one telephone number may be overrepresented in the sample.

• Registered voters who live in households consisting of more than one voter may be underrepresented.

• People who are not registered to vote may bias the sample results.

Publishers of a magazine wish to determine what proportion of the magazine's 50,000 subscribers are pleased with their subscription. The publishers intend to mail a survey to 1,000 subscribers randomly selected from those who have received the magazine for 5 years or more. This introduces selection bias, since long-subscribing customers are more likely to be pleased with their subscription. Which of the following would best eliminate selection bias?

• Mail surveys to 2,000 subscribers randomly selected from those who have received the magazine for 5 years or more.

• Mail surveys to 1,000 subscribers randomly selected from those who have received the magazine for 1 year or less.

• Mail surveys to 1,000 subscribers randomly selected from all subscribers.

• Mail surveys to 1,000 subscribers randomly selected from those who have received the magazine for 5 years or more and 1,000 subscribers randomly selected from those who have received the magazine for 1 year or less.

• Mail surveys to 500 subscribers randomly selected from a group who have received a free six-month subscription within the past year.