Exam 3: What Do Samples Tell Us

A recent survey of 174,745 randomly selected U.S. adults studied the importance of religion to Americans in each state. Of those questioned in the poll, 29 percent said that they were "moderately religious." The number 29 percent is a:

A confidence statement based on a probability sample says, "One can be 95 percent confident that between 72 percent and 78 percent of all adult Americans believe that the country needs a national health-care system." The phrase "95 percent confident" means that:

"Congress passed a ban on the sale of assault weapons. Now there is a move to repeal that ban. Do you agree that the ban on sale of assault weapons should be repealed?" That question is asked in an SRS of 1000 adults in Texas (population 18 million people) and a separate SRS of 1000 adults in Indiana (population 5.7 million people). Ninety-five percent confidence statements are made about the percents of all adults in both states who agree. The margin of error for Indiana is:

A recent survey asked a sample of 1010 people if they were baseball fans; 454 people in the sample said Yes. Assuming there is no bias, one can be 95 percent confident that the percent of all adults who are baseball fans is approximately between:

_____ in a sampling method means that the sample results will systematically misrepresent the population in the same way when one takes repeated samples.

A local planning commission is interested in finding out what proportion of its city's residents is opposed to constructing a new baseball stadium in the downtown area. A random sample of 1870 residents is obtained, and 41.2 percent of them are opposed to the stadium. In this sample, the proportion of the city's residents opposed to constructing a new baseball stadium in the downtown area is:

A local planning commission is interested in finding out what proportion of its city's residents is opposed to constructing a new baseball stadium in the downtown area. A random sample of 1870 residents is obtained, and 41.2 percent of them are opposed to the stadium. A 95 percent confidence interval was created for the proportion of the city's residents who are opposed to constructing a new baseball stadium in the downtown area. A "95 percent confidence" means that:

What is the most important issue facing the next president? In a January 2016 survey of 1022 adults, the Gallup organization found that Republicans and Democrats agreed on the top four issues, and terrorism was reported as the top challenge by 17 percent of respondents, with a margin of error of plus or minus 4 percentage points at 95 percent confidence level. There is a 95 percent confidence that between 13 percent and 21 percent of Americans feel that the most important issue facing the next president is terrorism. Increasing the sample size will:

A local planning commission is interested in finding out what proportion of its city's residents is opposed to constructing a new baseball stadium in the downtown area. A random sample of 1870 residents is obtained, and 41.2 percent of them are opposed to the stadium. In this sample, the margin of error is

The Gallup organization conducts a poll to see how much support there is for a constitutional amendment guaranteeing the right to abortion. They announce that 23 percent of Americans are in favor of such an amendment, with a 95 percent confidence margin of error of 3.4 percent. If the results of the above poll were described using a 90 percent confidence statement, what would happen to the margin of error?

The sports section of the East Mule Shoe Gazette runs a weekly question that readers can answer online. After the local university's football squad was beaten by its rival for the forty-second straight season, the question was "Do you think that the coach needs to go?" Of the 182 people who responded, 89 percent said Yes. The number 89 percent is a

Which of the following is correct?

What is the most important issue facing the next president? In a January 2016 survey of 1022 adults, the Gallup organization found that Republicans and Democrats agreed on the top four issues, and terrorism was reported as the top challenge by 17 percent of respondents, with a margin of error of plus or minus 4 percentage points at 95 percent confidence level. In this sample, the proportion of Americans who feel that the most important issue facing the next president is terrorism is:

If a sampling method is biased, then:

Does coaching raise SAT scores? Because many students score higher on a second try, even without coaching, a study looked at a simple random sample of 4200 students who took the SAT twice. Of these, 500 had taken coaching courses between their two attempts at the SAT. The study compared the average increase in scores (out of the total possible score of 2400) for students who were coached with the average increase for students who were not coached. The study is 95 percent confident that the difference between average scores for coached and uncoached students is between 28 and 57 points. To be 99 percent confident, the range of points would be:

What is the most important issue facing the next president? In a January 2016 survey of 1022 adults, the Gallup organization found that Republicans and Democrats agreed on the top four issues, and terrorism was reported as the top challenge by 17 percent of respondents, with a margin of error of plus or minus 4 percentage points at 95 percent confidence level. In this sample, the margin of error is:

A recent survey of 174,745 randomly selected U.S. adults studied the importance of religion to Americans in each state. The survey found that nationwide 40 percent said that they were very religious. But in New Hampshire, the least religious state, only 20 percent answered that they were "very religious." The sample included 1000 respondents from New Hampshire. The margin of error in a 95 percent confidence interval for the proportion of all adults who are very religious is:

Suppose somebody wishes to estimate the percentage of students who smoke cigarettes at each of several colleges and universities. Two of the colleges are Rice University (enrollment 6621) and Indiana University (enrollment 48,000). The margin of error for an SRS of 5 percent of the students at each school will be:

Do doctors in managed-care plans give less charity care? Researchers chose 60 communities at random and then chose doctors at random in each community. In all, they interviewed 10,881 doctors. Overall, 77.3 percent of the doctors said they had given some care free or at reduced rates because of the patient's financial need in the month before the interview. Doctors who received at least 85 percent of their practice income from managed-care plans were significantly less likely than other doctors to provide charity care. Some doctors who did not give any charity care may say that they did. If so, the study suffers from:

A Gallup Poll asked 1022 randomly chosen adults whether the failure of the government to solve major challenges facing the country was a "crisis," a "major problem," a "minor problem," or "not a problem." The proportion giving the response "a minor problem" was 14 percent. The margin of sampling error was plus or minus 3 percentage points. Assume a 95 percent confidence level and no bias. From the information given above, one can make which of the following statements? (Note that 14 percent ± 3 percent is 11 percent to 17 percent.)