Margin Of Error George Bush
Contents |
draw conclusions about populations. Gallup, for example, may survey about 1000 individuals to draw conclusions about millions. I. Important Concepts: Margin of Error Suppose a survey finds that 35% of the sample
Margin Of Error Formula
approves of the job performance of George Bush. This percentage, of course, is margin of error calculator just an estimate of the proportion in the population that approve of George Bush. How do we know close is that confidence interval calculator to the "true" proportion in the population? The margin of error provides a range in which the population (the "true") percentage falls--and gives an idea of how confident we can be that the population percentage falls within that margin. Most margins of error provided by pollsters are determined at about a 95% confidence level--that is, if you took an infinite number of samples, and from each sample calculated out a percentage of respondents that approved of Bush's performance as president, the "true" population percentage would fall within that range 95% of the time. A rough way to calculate margins of error at the 95% level is 100 divided by the square root of n (recall that n is your sample size). So, consider a hypothetical sample of 1,600 respondents. In the sample, about 40% of individuals approved of George Bush's job performance. What is the margin of error? The sample size is n=1600. The square root of the sample size is 40. So, 100/40 is the margin of error--we can say that the margin of error is + or - 2.5 percentage points We can also say that if you (hypothetically) took an infinite number of samples of respondents, and asked them the same questions, the "true" population percentage approval of Bush would fall in this range 95% of the time. Note a few things about the margin of error: First, the margin of error does not depend on the population size. So, if we have a sample size of 1,600, it doesn't matter if the population is 2000 or 4 million--the margin of error is the same. Second, the margin of error does depend on the sample size. The bigger the sample, the smaller the margin of error--and the narrower the range in which you're "95 confident" that the true, population percentage falls. Likewise, the smaller the sample, the less
engineering, see Tolerance (engineering). For the eponymous movie, see Margin for error (film). The top portion charts probability density against actual percentage, showing the relative probability that the actual percentage is realised, based on the sampled percentage. In the bottom portion, each line segment shows the 95% confidence interval of a sampling (with the margin of error on the left, and unbiased samples on the right). Note the greater the unbiased samples, the smaller the margin of error. The margin http://www.lsu.edu/faculty/bratton/7964/lecture4.htm of error is a statistic expressing the amount of random sampling error in a survey's results. It asserts a likelihood (not a certainty) that the result from a sample is close to the number one would get if the whole population had been queried. The likelihood of a result being "within the margin of error" is itself a https://en.wikipedia.org/wiki/Margin_of_error probability, commonly 95%, though other values are sometimes used. The larger the margin of error, the less confidence one should have that the poll's reported results are close to the true figures; that is, the figures for the whole population. Margin of error applies whenever a population is incompletely sampled. Margin of error is often used in non-survey contexts to indicate observational error in reporting measured quantities. In astronomy, for example, the convention is to report the margin of error as, for example, 4.2421(16) light-years (the distance to Proxima Centauri), with the number in parentheses indicating the expected range of values in the matching digits preceding; in this case, 4.2421(16) is equivalent to 4.2421 ± 0.0016.[1] The latter notation, with the "±", is more commonly seen in most other science and engineering fields. Contents 1 Explanation 2 Concept 2.1 Basic concept 2.2 Calculations assuming random sampling 2.3 Definition 2.4 Different confidence levels 2.5 Maximum and specific margins of error 2.6 Effect of population size 2.7 Other statistics 3 Comparing percentages 4
Have Margins of Error, Too Search Subscribe Now Log In 0 Settings Close search Site Search Navigation Search NYTimes.com Clear this text input Go Loading... See next articles See previous articles Site Navigation Site Mobile Navigation Advertisement Supported by http://www.nytimes.com/2000/11/19/weekinreview/the-election-surprise-elections-have-margins-of-error-too.html Week In Review The Election; Surprise! Elections Have Margins of Error, Too By GEORGE JOHNSONNOV. 19, 2000 Continue reading the main story Share This Page Continue reading the main story WITH its millions of microscopic switches silently clicking http://stat.psu.edu/~ajw13/stat500_su_res/notes/lesson06/lesson06_03.html half a billion times a second, the computer chip in a typical laptop could tally the presidential vote for the entire country in less than the blink of an eye. Its verdict would be flawless. All it is margin of doing, after all, is counting. No matter how voluminous and rapid its machinations, the chip must simply distinguish between 1's and 0's, the symbols of binary code. There are no shades of gray.Until Election Day 2000, the national electoral machine seemed very much like a huge, slow-motion computer chip. No matter how divided, each voter is finally forced into a binary decision, 1 or 0. The numbers are tallied up within each precinct, and when the margin of error precincts are totaled, the whole state flips. Determining who gets to be president is just a matter of arithmetic.The disquieting lesson this time around is that even something as seemingly trivial as counting is fraught with uncertainty and error. An election is like a poll: it has a margin of error. And if the margin is larger than the razor-thin difference of the vote, as seems likely in Florida, then the outcome will hinge on the tiniest chance perturbations. The president of the United States will be chosen at random.Every election is imperfect. Spread over a large enough pool of voters, the errors tend to cancel out, one here for Vice President Al Gore, one there for Gov. George W. Bush. And those that don't are swamped by the size of even a small electoral majority.But the closeness of the Florida vote has strained the system to the breaking point. Through a confluence of chance events -- ranging from mechanical glitches (the now infamous ''hanging chad'' throwing off automated ballot readers) to the zigzag trail of political and legal decisions that might have gone either way -- what the people of Florida really said may be not just uncertain but unknowable. Advertisement Continue reading the main story With so many variables, the vote may even be less accurate than a scientifically prepared poll, where the level of
Proportion Lesson 6.2 - Sample Size Computation and Minitab Commands to Compute Confidence Intervals for the Population Proportion Homework Lesson 6 Content Lesson 6.2 - Sample Size Computation and Minitab Commands to Compute Confidence Intervals for the Population Proportion Unit Summary Interpretation of Confidence Interval Margin of Error Determining the Required Sample Size Minitab Commands to Find the Confidence Interval for a Population Proportion Reading Assignment An Introduction to Statistical Methods and Data Analysis, chapter 10.2. Interpretation of Confidence Interval (read page 197 in your textbook) In the graph below, we draw 10 replications (for each replication, we sample 30 students and ask them whether they are Democrats) and compute the 80% Confidence Intervals each time. We are lucky in this set of 10 replications and get exactly 8 out of 10 intervals that contain the parameter. Due to the small number of replications (only 10), it is quite possible that we get 9 out of 10 or 7 out of 10 that contain the true parameter. On the other hand, if we try it 10,000 (a large number of) times, the percentage that contains the true porportions will be very close to 80%. If we repeatedly draw random samples of size n from the population where the proportion of success in the population is and calculate the confidence interval each time, we would expect that 100(1 - )% of the intervals would contain the true parameter, . Margin of Error Note: The margin of error E is half of the width of the confidence interval. Confidence and precision (we call wider intervals as having poorer precision): Note that the higher the confidence level, the wider the width (or equivalently, half width) of the interval and thus the poorer the precision. One television poll stated that the recent approval rating of President Geroge Bush is 72%; the margin of error of the poll is plus or minus 3%. [For most newspapers and magazine polls, it is understood that the margin of error is calculated for a 95% confidence interval (if not stated otherwise). A 3% margin of error is a popular choice.] If we want the margin of error smaller (i.e., narrower intervals), we can increase the sample size. Or, if you calculate a 90% confidence interval instead of a 95% confidence interval, the margin of error will also be smaller. However, when one reports it, remember to state that the confidence interval is only 90% because otherwise people will assume a 95% confidence. Determining the Required Sample Size If the desired margin of error E is specified and th