## Understanding Confidence Intervals in Poll ResultsA newspaper article about the results of a poll states:"In theory, the results of such a poll, in 99 cases out of 100, should differ by no more than 5 percentage points in either direction from what would have been obtained by interviewing all voters in the United States."To analyze this, we need to find the sample size suggested by this statement.### Task**a.** Shade and label the missing parts in the graph for a 99% confidence interval. You may use Excel or a calculator to find the *z*-score. Round the *z*-score to two decimal places.### DiagramThe diagram is a standard normal distribution curve:- **Area to the left = ____**- **Area in the middle = ____**- **Area to the right = ____**- **z = ____****b.** Determine the sample size.This exercise involves understanding the concept of confidence intervals, critical values (*z*-scores), and using them to determine the sample size needed to ensure the poll's accuracy within a specified margin of error (5 percentage points in this case).

Answered: 9) A newspaper article about the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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26. You are trying to figure out if there is interest in a new restaurant opening in town. You speak to 150 random people, and discover that 60 of them would visit the new restaurant. Find a 95% confidence interval for the proportion of people that would visit the new restaurant.
4.
Now, let's imagine the poll that found that 52% of U.S. adults believe that the federal government has too much power. And let's say the poll was conducted via telephone interviews among 1010 U.S. adults and contained a margin of error of 2 percentage points at the 95% confidence level. Question 5 Use the information above to create an interval estimate for the proportion of all U.S. adults who believe that the federal government has too much power. %, I don't know %) You answered 4 out of 4 correctly. Asking up to 5. Last attempt
A Gallup survey based on telephone and face-to-face interviews with 4,220 adults in China, aged 15 and older suggests that 30% smoke regularly or occasionally. The following is also noted "one can say with 95% confidence that the maximum margin of sampling error is 2.2 percentage points". Which of the following is true based on the results of this survey? a. We are 95% confident that 27.8 % to 32.2 % of all Chinese adults smoke. b. If the sample size was larger, the margin of error would be larger as well. c.We are 95% confident that 25.6% to 34.4% of all Chinese adults smoke. d. Exactly 30% of all Chinese adults smoke. e. If we were to randomly sample another group of 4,220 Chinese adults we would find that exactly 30% of them smoke as well.
Suppose that in a recent poll, 550 of the 915 randomly selected U.S. adults agreed with the statement “social media sites like Facebook and Twitter do more to divide the country” (as opposed to unite the country, or neither). a. Use this information to construct a 90% confidence interval.
Suppose a 90 percent confidence interval to estimate a population proportion was calculated from a sample proportion of 18 percent and a margin of error of 4 percent. What is the width of the confidence interval?
9. A researcher wants to construct a 99% confidence interval for the proportion of Americans who think that the U.S. invading Iraq was an effective step in combating world terrorism. She has no initial idea of what that proportion is. How large should her sample size be if she wants the margin of error to be at most two percent? Show or explain your thinking.
Here is an explanation from the Associated Press concerning one of its opinion polls. Explain briefly but clearly in what way this explanation is incorrect. For a poll of 1,600 adults, the variation due to sampling error is no more than three percentage points either way. The error margin is said to be valid at the 95 percent confidence level. This means that, if the same questions were repeated in 20 polls, the results of at least 19 surveys would be within three percentage points of the results of this survey.
2. Bob draws a simple random sample from an extremely large population of lemons. The sample size is n=700 and in the sample 250 lemons turn out to be good and 450 lemons turn out to be bad. Find the 95% confidence interval for the population proportion p of good lemons.
3. Bob draws a simple random sample from an extremely large population of lemons. The sample size is n=925 and in the sample 576 lemons turn out to be good and 349 lemons turn out to be bad. Find the 99% confidence interval for the population proportion P of good lemons.

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