Margin Of Error Notes
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Margin Of Error Calculator
review Statistics AP study guides Probability Survey sampling Excel Graphing calculators Book reviews Glossary AP practice exam Problems margin of error excel and solutions Formulas Notation Share with Friends Margin of Error In a confidence interval, the range of values above and below the sample statistic is called the margin of
Margin Of Error Confidence Interval Calculator
error. For example, suppose we wanted to know the percentage of adults that exercise daily. We could devise a sample design to ensure that our sample estimate will not differ from the true population value by more than, say, 5 percent (the margin of error) 90 percent of the time (the confidence level). How to Compute the Margin of margin of error definition Error The margin of error can be defined by either of the following equations. Margin of error = Critical value x Standard deviation of the statistic Margin of error = Critical value x Standard error of the statistic If you know the standard deviation of the statistic, use the first equation to compute the margin of error. Otherwise, use the second equation. Previously, we described how to compute the standard deviation and standard error. How to Find the Critical Value The critical value is a factor used to compute the margin of error. This section describes how to find the critical value, when the sampling distribution of the statistic is normal or nearly normal. The central limit theorem states that the sampling distribution of a statistic will be nearly normal, if the sample size is large enough. As a rough guide, many statisticians say that a sample size of 30 is large enough when the population distribution is bell-shaped. But if the original population is badly skewed, has multiple peaks, and/or has outliers, researchers like the sam
accurate, assuming you counted the votes correctly. (By the way, there's a whole other topic in math that describes the errors people can make when they try to measure things like that. But, for now, let's
Margin Of Error In Polls
assume you can count with 100% accuracy.) Here's the problem: Running elections costs a lot of
Margin Of Error Sample Size
money. It's simply not practical to conduct a public election every time you want to test a new product or ad campaign. So margin of error vs standard error companies, campaigns and news organizations ask a randomly selected small number of people instead. The idea is that you're surveying a sample of people who will accurately represent the beliefs or opinions of the entire population. But how many people http://stattrek.com/estimation/margin-of-error.aspx do you need to ask to get a representative sample? The best way to figure this one is to think about it backwards. Let's say you picked a specific number of people in the United States at random. What then is the chance that the people you picked do not accurately represent the U.S. population as a whole? For example, what is the chance that the percentage of those people you picked who said their favorite color was blue http://www.robertniles.com/stats/margin.shtml does not match the percentage of people in the entire U.S. who like blue best? Of course, our little mental exercise here assumes you didn't do anything sneaky like phrase your question in a way to make people more or less likely to pick blue as their favorite color. Like, say, telling people "You know, the color blue has been linked to cancer. Now that I've told you that, what is your favorite color?" That's called a leading question, and it's a big no-no in surveying. Common sense will tell you (if you listen...) that the chance that your sample is off the mark will decrease as you add more people to your sample. In other words, the more people you ask, the more likely you are to get a representative sample. This is easy so far, right? Okay, enough with the common sense. It's time for some math. (insert smirk here) The formula that describes the relationship I just mentioned is basically this: The margin of error in a sample = 1 divided by the square root of the number of people in the sample How did someone come up with that formula, you ask? Like most formulas in statistics, this one can trace its roots back to pathetic gamblers who were so desperate to hit the jackpot that they'd even stoop to mathematics for an "edge." If you really want to know the
statistics are much better at targeting these values and consequently yield better results. Statistics that are better at targeting population parameters are mean, proportion, variance and to a lesser degree standard deviation. We will be concentrating on the first two of http://mathbitsnotebook.com/Algebra2/Statistics/STmarginError.html these statistics. Confidence Intervals and Levels: Once we have created our sampling distribution of the sample statistic, and arrived at our best estimate of the parameter of the population, we need to reveal just how good this estimate may be. Instead of simply stating the estimate as a single value, statisticians form intervals surrounding the estimate. These intervals are called confidence intervals (or interval estimates). A confidence interval is a range, or interval, of values margin of used to estimate the true value of a population parameter. Confidence intervals are associated with confidence levels, such as 95%, which tell us the percentage of times the confidence interval actually contains the true population parameter we seek. The distance from the estimate to one end of a confidence interval is referred to as the margin of error (MOE). If you want to make a confidence interval smaller, increase the sample size. Note: Correct statement: margin of error "We are 95% confident that the interval from 0.468 to 0.579 actually contains the true value of the population proportion." Incorrect statement: "There is a 95% chance that the true value of the population proportion lies between 0.468 and 0.579." The first refers to a 95% success rate of the process used. The second refers to the proportion itself. Dealing with Proportions • For ALL possible samples of the same size, n, from the same population, the graph of the sampling distribution of sample proportions will resemble a Normal curve with a mean equal to the value of the true population proportion. Notations: population mean = μ (mu) population proportion = p population standard deviation = σ sample mean = (x-bar) sample proportion = (p-hat) sample standard deviation = s • Standard error (SE) is the standard deviation of the sampling distribution of a statistic (for proportions, ). • To obtain the margin of error (MOE) for working with a sample proportion, we need to address the Confidence Level needed in the problem (such as 95%). To do this, multiply the standard error by the critical value associated with the desired Confidence Level (see chart at the right and read the NOTE). For a confidence level of 95%, we use the formula: Since we are familiar with 95% being associated with ±2 standar
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