Analyzing Samples

Google places opinion poll questions next to many of its news stories. Simply click your response to join the sample. One of the questions in January 2018 was "Do you plan to diet this year?" More than 30,000 people responded, with 68% saying "Yes." You can conclude that

• about 68% of Americans planned to diet in 2018

• the poll used a convenience sample, so the results tell us little about the population of all adults

• the poll uses voluntary response, so the results tell us little about the population of all adults

• the sample is too small to draw any conclusion

• none of these

To gather information about the validity of a new standardized test for tenth-grade students in a particular state, a random sample of 15 high schools was selected from the state. The new test was administered to every 10th-grade student in the selected high schools. What kind of sample is this?

• Simple random sample

• Stratified random sample

• Cluster sample

• Systematic random Sample

• Voluntary response sample

Your statistics class has 30 students. You want to call an SRS of 5 students from your class to ask where they use a computer for the online quizzes. You label the students 01, 02, ... , 30. You enter the table of random digits at this line:

14459 26056 31424 80371 65103 62253 22490 61181

Your SRS contains the students labeled

• 14, 45, 92, 60, 56

• 14, 31, 03, 10, 22

• 14, 03, 10, 22, 22

• 14, 03, 10, 22, 06

• 14, 03, 10, 22, 11

Suppose that 35% of the registered voters in a state are registered as Republicans, 40% as Democrats, and 25% as independents. A newspaper wants to select a sample of 1000 registered voters to predict the outcome of the next election. If they randomly select 350 Republicans, randomly select 400 Democrats, and randomly select 250 Independents, did the sampling procedure result in a simple random sample of registered voters from this district?

• Yes, because each registered voter had the same chance of being chosen

• Yes, because random chance was involved

• No, because not all registered voters had the same chance of being chosen

• No, because there were a different number of registered voters selected from each party

• No, because not all possible groups of 1000 registered voters had the same chance of being chosen

A local news agency conducted a survey about unemployment by randomly dialing phone numbers until they had gathered responses from 1000 adults in their state. In the survey, 19% of those who responded said they were not currently employed. In reality, only 6% of the adults in the state were not currently employed at the time of the survey. Which of the following best explains the difference in the two percentages?

• The difference is due to sampling variability. We shouldn't expect the results of a random sample to match the truth about the population every time.

• The difference is due to response bias. Adults who are employed are likely to lie and say that they are unemployed.

• The difference is due to undercoverage bias. The survey included only adults and did not include teenagers who are eligible to work.

• The difference is due to nonresponse bias. Adults who are employed are less likely to be available for the sample than adults who are unemployed.

• The difference is due to voluntary response. Adults are able to volunteer as a member of the sample.

A simple random sample of 1200 adult Americans is selected, and each person is asked the following question: "In light of the huge national deficit, should the government at this time spend additional money to establish a national system of health insurance?" Only 39% of those responding answered "Yes." This survey

• is reasonably accurate since it used a large simple random sample

• needs to be larger since only about 24 people were drawn from each state

• probably understates the percent of people who favor a system of national health insurance

• is very inaccurate but neither understates nor overstates the percent of people who favor a system of national health insurance. Because simple random sampling was used, it is unbiased

• probably overstates the percent of people who favor a system of national health insurance