quiz 3

A Gallup Poll asked, "What is your favorite Summer Olympics event?" Of the people asked, 27 percent said, "swimming." Here is what Gallup says about the accuracy of this poll: The results are based on telephone interviews with a sample of 1007 national adults, aged 18 years and older. For results based on the total sample of national adults, one can say with 95 percent confidence that the maximum error attributable to sampling and other random effects is plus or minus 3 percentage points. In addition to sampling error, question wording and practical difficulties in conducting surveys can introduce error or bias into the findings of public opinion polls. Suppose 500 people in the sample of 1007 adults were women. Gallup asked these 500 women, "What is your favorite Summer Olympic event?" Thirty-five percent said swimming was their favorite. Gallup gave a margin of error for this result. This margin of error is:

greater than plus or minus three points because the sample for this question is smaller.

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 ìDo you think that the coach needs to go?î Of the 182 people who responded, 89 percent said Yes. The number 89 percent is a: margin of error. parameter. reliability. statistic.

statistic.

To reduce the variability of estimates from a simple random sample, one should: use a smaller sample. increase the bias. use a percent, not a count. use a count, not a percent. use a larger sample.

use a larger sample.

A Gallup Poll asked, "What is your favorite Summer Olympics event?" Of the people asked, 27 percent said, "swimming." Here is what Gallup says about the accuracy of this poll: The results are based on telephone interviews with a sample of 1007 national adults, aged 18 years and older. For results based on the total sample of national adults, one can say with 95 percent confidence that the maximum error attributable to sampling and other random effects is plus or minus 3 percentage points. In addition to sampling error, question wording and practical difficulties in conducting surveys can introduce error or bias into the findings of public opinion polls. Suppose 500 people in the sample of 1007 adults were women. Gallup asked these 500 women, "What is your favorite Summer Olympic event?" Thirty-five percent said swimming was their favorite. Gallup gave a margin of error for this result. Applying the quick method, one finds that the margin of error for 95 percent confidence changes when the sample size drops from 1007 to 500, from: 3.2 percent to 4.5 percent. 3 percent to 1.5 percent. 4.5 percent to 3.2 percent. 3 percent to 6 percent.

3.2 percent to 4.5 percent.

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. If one applied the quick method to the poll, one would obtain this 95 percent confidence interval: 182 ± 7% 89% ± 18% 82% ± 7% 89% ± 7%

89% ± 7%

When an opinion poll says that "with 95 percent confidence," and the margin of error for its results is plus or minus 3 percentage points, this means that: one can be certain that the true population value is within ± 3 points of 95 percent. 95 percent of the people chosen for the sample were contacted. 95 percent of all samples chosen, as this one was, give results within ± 3 points of the true population value. the percent of people who said Yes to the question was between 92 percent and 98 percent. between 92 percent and 98 percent of the people chosen for the sample were contacted.

95 percent of all samples chosen, as this one was, give results within ± 3 points of the true population value.

_____ in a sampling method means that the sample results will systematically misrepresent the population in the same way when one takes repeated samples. Confidence level Comparison Confounding Bias Variability

Bias

A Gallup Poll asked, "What is your favorite Summer Olympics event?" Of the people asked, 27 percent said, "swimming." Here is what Gallup says about the accuracy of this poll: The results are based on telephone interviews with a sample of 1007 national adults, aged 18 years and older. For results based on the total sample of national adults, one can say with 95 percent confidence that the maximum error attributable to sampling and other random effects is plus or minus 3 percentage points. In addition to sampling error, question wording and practical difficulties in conducting surveys can introduce error or bias into the findings of public opinion polls. Which of these is a correct confidence statement based on this Gallup Poll, assuming there is no bias? Incorrect Response Gallup is 95 percent confident that between 24 percent and 30 percent of the 1007 people interviewed would say swimming is their favorite Summer Olympic event. Among many samples, 95 percent will find that 27 percent of the people interviewed will say swimming is their favorite Summer Olympic event. Correct Answer Gallup is 95 percent confident that between 24 percent and 30 percent of all adults would say swimming is their favorite Summer Olympic event. There is a 95 percent chance that the opinions of the 1007 people interviewed fairly represent the opinions of all adults.

Gallup is 95 percent confident that between 24 percent and 30 percent of all adults would say swimming is their favorite Summer Olympic event.

Which of the following is correct? Parameters describe sample characteristics. The population is a subset of the sample. Parameters describe population characteristics. Statistics must be based on a simple random sample.

Parameters describe population characteristics.

Which of the following is correct? Statistics describe population characteristics. Statistics describe sample characteristics. The population is a subset of the sample. Parameter and statistic are two names for the same thing.

Statistics describe sample characteristics.

"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. It would be cheaper to just announce the question on TV and ask people to call in with their opinions. Is this the best approach? This is a good way to get information about the opinions of all adults. This is a bad idea because those who call in would not be a population. This is a bad idea because those who call in would not be a sample. This is a bad idea because allowing people to volunteer may result in large bias. This is a bad idea because if only a few people call in, the margin of error will be large.

This is a bad idea because allowing people to volunteer may result in large bias.

_____ in a sampling method describes how spread out the values of the sample statistic are when one takes repeated samples. Confounding Bias Variability Confidence level

Variability

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. The number 77.3 percent is: a statistic because it describes a sample. a statistic because it describes a population. a parameter because it describes a sample. a parameter because it describes a population.

a statistic because it describes a sample.

When constructing a confidence interval, the "margin of error" means that if there is no bias: about half of the samples taken will come at least this close to the truth. the sampling method is biased. Otherwise, the poll would always give the correct answer. there are serious non-sampling errors. Otherwise, the poll would always give the correct answer. every sample taken will come at least this close to the truth. about 95 percent of all samples taken will come at least this close to the truth.

about 95 percent of all samples taken will come at least this close to the truth.

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 large margin of error to take account of possible failure to be truthful. sampling errors that require a better random sampling design. bias: The sample result will systematically underestimate the true percent of doctors who give charity care. bias: The sample result will systematically overestimate the true percent of doctors who give charity care.

bias: The sample result will systematically overestimate the true percent of doctors who give charity care.

A Gallup Poll asked, "What is your favorite Summer Olympics event?" Of the people asked, 27 percent said, "swimming." Here is what Gallup says about the accuracy of this poll: The results are based on telephone interviews with a sample of 1007 national adults, aged 18 years and older. For results based on the total sample of national adults, one can say with 95 percent confidence that the maximum error attributable to sampling and other random effects is plus or minus 3 percentage points. In addition to sampling error, question wording and practical difficulties in conducting surveys can introduce error or bias into the findings of public opinion polls. In Gallup's statement, "95 percent confidence" means (assuming there is no bias) that: Gallup knows 95 percent of all adults would give the same answer that this poll found. this poll is one of the 95 percent of all Gallup polls that give correct results. if Gallup were to repeat this poll many times, 95 percent of the results would be within plus or minus 3 percentage points of the truth about the population. if Gallup were to repeat this poll many times, 95 percent of all the polls would find that 27 percent of the people interviewed would say swimming is their favorite Summer Olympic event.

if Gallup were to repeat this poll many times, 95 percent of the results would be within plus or minus 3 percentage points of the truth about the population.

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: larger for Rice than for Indiana. about the same at both schools. either smaller or larger for Rice. It isn't possible to tell without seeing the sample results. smaller for Rice than for Indiana.

larger for Rice than for Indiana.

If a Gallup Poll surveys a national sample of 3000 people rather than 1500 people, the margin of error of the sample result would be: less than it would be for 1500 because the sample is now larger. greater than it would be for 1500 because the sample is now larger. the same as for 1500 because the population is the same. either less or greater than it would be for 1500. It's impossible to say, because sample size 3000 is not in the table. either less or greater than it would be for 1500 because it depends on the chance outcome of the sample.

less than it would be for 1500 because the sample is now larger.

If a sampling method is biased, then: one needs to increase the sample size to remove the bias. one needs to improve the sampling method to remove the bias. the center of the distribution of the statistic will be close to the population parameter. the sample statistic will be close to the population parameter. one should sample from a larger population.

one needs to improve the sampling method to remove the bias.

If the sample size is much smaller than the population size, the margin of error of a simple random sample depends on: both of the above. sample size. population size. neither of the above.

sample size.

If one were to choose an SRS from a population, one could be sure that the _____, computed from the SRS, is a(n) _____ estimate of the population's true _____. One also knows that one can reduce the _____ of the result as desired, by taking a large enough sample. parameter; variation; statistic; unbiasedness statistic; unbiased; parameter; variation parameter; unbiased; statistic; variation statistic; variation; parameter; unbiasedness

statistic; unbiased; parameter; variation

Increasing the size of an SRS has these beneficial effects: both A and B are correct. the bias of the sample is reduced relative to smaller SRSs. nonsampling errors become less important. the margin of error is smaller than it is for smaller SRSs. answers A, B, and C are correct.

the margin of error is smaller than it is for smaller SRSs.

"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: smaller because everything is bigger in Texas. larger than in Texas because there are fewer people in Indiana. the same as in Texas because the two SRSs are the same size. smaller than in Texas because there are fewer people in Indiana. may be either smaller or larger than in Texas because the sample result varies due to chance.

the same as in Texas because the two SRSs are the same size.

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 report of the SAT study says, "With 95 percent confidence, one can say that students who are coached raise their average SAT scores by between 28 and 57 points more than students who are not coached." By "95 percent confidence," the report means that: 95 percent of all students will increase their score by between 28 and 57 points if they are coached. the average increase is between 28 and 57 points. the study obtained the 28 to 57 point range by using a method that would give a correct answer in 95 percent of all samples. 95 percent of all adults would believe the statement.

the study obtained the 28 to 57 point range by using a method that would give a correct answer in 95 percent of all samples.

If one takes many simple random samples from the same population, one expects: the values of the statistic will vary from sample to sample. the same values of the statistic for each sample. a different value of the parameter for each sample. a problem with voluntary response. a problem with bias.

the values of the statistic will vary from sample to sample.

The margin of error for a poll is 4 percent. This means that: 4 percent of the population was in the sample. 4 percent of those sampled gave the wrong answer to the question asked. 4 percent of those sampled did not answer the question asked. there is a 95 percent confidence that the sample statistic is within 4 percent of the population parameter.

there is a 95 percent confidence that the sample statistic is within 4 percent of the population parameter.

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: narrower because higher confidence requires a smaller margin of error. narrower because higher confidence requires a larger margin of error. wider because higher confidence requires a smaller margin of error. wider because higher confidence requires a larger margin of error.

wider because higher confidence requires a larger margin of error.

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. For a simple random sample of size 10,881, the margin of error for 95 percent confidence is about: 9.6%. ± 3%. ± 0.0096%. ± 0.96%.

± 0.96%.

For a simple random sample of size 4761, the margin of error for 95 percent confidence is about: ± 0.00021%. ± 0.021%. ± 0.0145%. ± 1.45%.

± 1.45%.

Before the 2016 presidential election, a national survey asked a sample of 2009 American adults what kind of president Donald Trump would be: 52 percent said "poor" or "terrible." The margin of error announced by news reports of this poll was approximately: ± 2% ± 6% ± 0.02% ± 3% ± 4%

± 2%