Indiana has a population of about 7 million people and Ohio about 12 million. Is itpossible for there to be a poll where over 50% of Hoosiers say "yes", over 50% ofOhioans say "yes", but over 50% of all residents of both states say "no"? If no, explainwhy not. If yes, give an example of how that could happen.

Answered: Indiana has a population of about 7…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A survey of Hoosiers found that 47%47% are Pacers fans, 54%54% are Colts fans, and 25%25% are Pacers fans but not Colts fans. What proportion of those surveyed are Colts fans but not Pacers fans?
The true proportion of voters in favor of a candidate is unknown. A random sample of 329 voters results in 104 "Yes" responses (i.e. in favor of the candidate). Find the point estimate for the true population proportion of voters who favor the candidate.
2. Are attitudes toward shopping changing? Sample surveys show that fewer people enjoy shopping in stores than in the past. A recent survey asked a random sample of 2500 U.S. adults if they agreed or disagreed with the statement, "I prefer to shop for clothes online rather than in a store." In this survey, 1575 agreed. A manager of a local clothing store claims that 60% of all U.S. adults would say "Agree" if asked the same question. (a) What is the sample proportion of U.S. adults who agreed with the statement? (b) If the manager's claim is true, what is the probability that the proportion in a random sample of 2500 U.S. adults is at least as far above 0.60 as the results of this survey? (c) Based on your answer in part (b), do you have reason to doubt the manager's claim?
You are doing a research project in political science to determine the proportion of voters in your district who favor capital punishment. a. If no preliminary sample of voters is taken to estimate p, how large a sample is necessary to be 99% sure that the point estimate will be within a distance of .01 from p? b. The NORC found that approximately 67% of people in the U.S. favor capital punishment. How large a sample is necessary to be 99% sure that the point estimate will be within a distance of .01 from p?
Dr. A. Ventura is interested in determining what kinds and how many pets people own in Bakersfield. He stands outside Petco and asks people what kind of pet they own. This is the result of his survey: dog=1; cat=2; bird=3; reptile=4; fish=5; other=6 1,1,2,2,2,1,1,3,2,3,1,1,1,2,2,4,4,2,2,1,1,1,5,4,3,4,1,1,1,2,2,6,1,1,2,2,1,2,1,2,6,3,4,5
A senator wishes to estimate the proportion of United States voters who favor abolishing the electoral college. how large a sample is needed in order to be 98% confident that the sample proportion will not differ from the true proportion by more than 3%?
The results of a survey of visitors at the Eiffel Tower showed that 25 spoke English, 15 spoke French, and 8 spoke both English and French. How many spoke English or French?
Wegman’s (a food market chain) has developed a new store-brand brownie mix. Before they start selling the mix they want to compare how well people like their brownies to brownies made from a popular national brand mix. In order to see if there was any difference in consumer opinion, Wegman’s asked 124 shoppers to participate in a taste test. Each was given a brownie to try. Subjects were not told which kind of brownie they got—that was determined randomly. 58% of the 62 shoppers who tasted a Wegman’s brownie said liked it well enough to buy the mix, compared to 66% of the others who said they would be willing to buy the national brand. Does this result indicate that consumer interest in the Wegman’s mix is lower than for the national brand?
5. 43% of the students in a school are boys. If there are 399 girls in the school, what is the entire population of the school? [2]
In politics, marketing, etc. we often want to estimate a percentage or proportion p. One calculation in statistical polling is the margin of error - the largest (reasonble) error that the poll could have. For example, a poll result of 72% with a margin of error of 4% indicates that p is most likely to be between 68% and 76% (72% minus 4% to 72% plus 4%). In a (made-up) poll, the proportion of people who like dark chocolate more than milk chocolate was 39% with a margin of error of 1.3%. Describe the conclusion about p using an absolute value inequality. The answer field below uses the symbolic entry option in Mobius. That lets you type in a vertical bar | to represent absolute values. Also, when you type in < and then =, the symbolic entry option will automatically convert that to ≤ . In the same way, if you type in > and then =, the symbolic entry option will automatically convert that to ≥. Be sure to use decimal numbers in your answer (such as using 0.40 for 40%).
The accompanying table shows the result of a national election along with the vote predicted by several organizations in the days before the election. The sample sizes were typically a bit above 1,000 people, and the reported margin of error was around plus or minus 4 percentage points. The percentages for each poll may not sum to 100 because of voters who indicated they were undecided. Complete parts a through c. Click the icon to view the vote predictions and result. a. The News Network 1 poll predicted that 49% were going to vote for Candidate A, with a margin of error of plus or minus 4%. Explain what this means. Select the correct choice below and fill in the answer boxes to complete your choice. (Type integers or decimals. Do not round.) O A. The true proportion of voters for Candidate A is within percentage points of %. O B. The actual proportion of voters for Candidate A is likely to be more than percentage points away from O C. All samples have a sample proportion that is…
A pollster wishes to estimate the proportion of United States voters who favor capital punishment. How large a sample is needed in order to be 90% confident that the sample proportion will not differ from the true proportion by more than 5%?

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