Use this information to answer the next two questions.A Gallup Poll found that 51% of the people in its sample said "yes" when asked, "Would you like to lose weight?" Gallup announced: "With 95% confidence for results based on the total sample of national adults, one can say that the margin of sampling error is ± 3%."
1. What is the 95% confidence interval estimate for the percent of all adults who want to lose weight?
(45%, 57%)
(48%, 54%)
(51%, 54%)
(48%, 51%)
2. Interpret "95% confidence" for this situation.
95% of the time, 51% will be in the interval computed in the previous question.
95% of the confidence intervals, computed from the results of all possible samples of the same size, will contain the true percentage of all national adults who want to lose weight.
95% of the responses from the national adults in the sample will be in the interval computed in the previous question.
95% of the time, the percentage of all national adults who want to lose weight (i.e., the value of the parameter) will be in the interval computed in the previous question.
3. A New York Times poll on women's issues interviewed 1025 women randomly selected from the United States, excluding Alaska and Hawaii. The poll found that 47% of the women said they do not get enough time for themselves. The poll announced a margin of error of ± 3% for 95% confidence in its conclusions. What does this margin of error account for?
sampling variability
measurement errors
non-random sampling
non-normal data
bias due to undercoverage, non-response, question wording, etc.
4. Data from a simple random sample of 2000 adults in California were used to compute a 90% confidence interval for the proportion of adults that favor the death penalty. Data from a simple random sample of 2000 adults in Idaho were also used to compute a 90% confidence interval for the proportion of adults that favor the death penalty. The population of California is 39 million and the population of Idaho is 2 million. Suppose that the calculated sample proportions are equal for the two samples.The margin of error of the confidence interval for Idaho is
smaller than that of California.
smaller or larger than for California, depending on chance variation.
greater than that of California.
the same as for California.
Use this information to answer the next four questions.Publishing scientific papers online is fast, and the papers can be long. Publishing in a paper journal means that the paper will live forever in libraries. The British Medical Journal combines the two: it prints short and readable version, with longer versions available online. Is this okay with authors? The journal asked a random sample of 104 of its recent authors the question, "Should the journal continue using this system?" In the sample, 72 said "yes".
5. Were the data collected appropriately for estimating proportion with a large-sample confidence interval for a proportion?
Yes, because the British Medical Journal randomly selected 104 of its recent authors, making this an SRS.
No, because even though the sample was randomly selected, recent authors were selected from those with a short version of their paper and those with a long version of their paper, making this a stratified sample and not an SRS.
No, because the recent authors were selected from two strata: those who say that it is okay to publish two versions and those who say that it is not. That makes this a stratified sample and not an SRS.
Yes, because a large-sample confidence interval for a proportion can be used even when the data are not collected with an SRS.
6. Is the sample size large enough for estimating a population proportion with a large-sample confidence interval?
Yes, because the sample size exceeds 30.
No, because number of those responding "no" is less than 10.
Yes, because both np-hat and n(1 - p-hat) are greater than 10.
No, because the number of those responding "yes" is less than 10.
Yes, because the number of journals published exceeds 30.
7. Assuming the conditions are met, what is the value of the standard error of p-hat?
0.0452
0.0020
0.6923
0.2130
0.0180
8. Assuming the conditions are met, if the 95% confidence interval for p was calculated to be (0.604, 0.781), what is the correct interpretation for this interval?
We are 95% confident that the proportion of all recent authors who agree with publishing two versions is somewhere between 60.4% and 78.1%.
There is a 95% chance that p, the proportion of all recent authors who agree with publishing two versions, is contained in the interval (0.604, 0.781).
95% of the proportions of recent authors in surveys of size 104 who agree with publishing two version are between 0.604 and 0.781.
There is a 95% chance that p-hat, the proportion of authors surveyed who agree with publishing two versions, is contained in the interval (0.604, 0.781).
Use this information to answer the next two questions.Suppose that a survey of physicians is being designed to estimate the proportion of primary-care physicians who have participated in some sort of doctor-assisted suicide. This survey aims to estimate the proportion within 0.05 with 95% confidence.
9. How many primary-care physicians should be randomly sampled?
97
769
1537
400
10. The researchers decided that it was too expensive to sample as many as was required from their calculations. What could they do to decrease the required sample size and therefore the cost?
Increase their confidence level
Decrease their confidence level
Decrease their desired margin of error