For A Given Sample Size Reducing The Margin Of Error
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For A Specified Confidence Level Larger Samples Provide Smaller Margins Of Error
alexxspencerr STUDY STUDY ONLY Flashcards Flashcards Learn Learn Spell Spell Test Test for a fixed margin of error larger samples provide greater confidence PLAY PLAY ONLY Match Match PLAY PLAY ONLY Match Match Gravity Gravity {loginLink} to add this set to for a certain confidence level you can get a smaller margin of error by selecting a bigger sample a folder Log in to add this set to a class. Share this set Share on Facebook Share on Twitter Share on Google Classroom Send Email Short URL List Info Like
Making A Type Ii Error Is Only Possible If The Null Hypothesis Is True.
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accurate, assuming you counted the votes correctly. (By the way, there's a whole other topic in math that describes the the paralyzed veterans of america is a philanthropic organization that relies on contributions errors people can make when they try to measure things like that. But,
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for now, let's assume you can count with 100% accuracy.) Here's the problem: Running elections costs a lot of margin of error and confidence level money. It's simply not practical to conduct a public election every time you want to test a new product or ad campaign. So companies, campaigns and news organizations ask a randomly selected https://quizlet.com/18778612/statistics-chapter-19-20-review-flash-cards/ 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 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 http://www.robertniles.com/stats/margin.shtml 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 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 th
a response to the following: You are a political consultant who has been asked to predict the winner in what is expected to be a very close race for a https://www.math.lsu.edu/~madden/M1101/student_work/margin_of_error.html senate seat. There are two candidates: a democrat and a republican. A https://onlinecourses.science.psu.edu/stat100/node/17 previous poll of a random sample of people who are likely to vote has found 49% of the sample favor the democrat. The poll has a reported margin of error of plus or minus 4%, at 95% confidence. Explain how you might use a computer simulation to determine how large a sample of error you would need to reduce the margin of error to 2%. If the poll were repeated with a sample of this size, would you necessarily get a better basis for predicting a winner? Here is what they said. Student responses are in black. My remarks are in red. To see how I would have answered, look at the end of this document. -In order to margin of error reduce the margin of error, increase the number of people polled along with the number of samples. More individuals in a sample, or more samples, both will yield more information. But when we speak of "margin of error," we generally mean to refer to a single sample. -Yes. With each time (averaged w/ the others), the margin of error as well as the confidence would increase. You should note that there is a tradeoff between margin of error and level of confidence. Even with a single sample, your margin of error can be made smaller at the expense of confidence. -In order to gain a 2% margin of error, you must sample a large enough group of the population. You must sample until less than 5% of the sample group is further away than 2% from the target value. This statement doesn't make any sense in the context. The sampled units are being tested to see if they are democrats or republicans. How could an individual be "2% from the target value"? The previous sentence is a misunderstanding of what is meant by level of confidence. The correct idea is: we m
discussed in the previous section, the margin of error for sample estimates will shrink with the square root of the sample size. For example, a typical margin of error for sample percents for different sample sizes is given in Table 3.1 and plotted in Figure 3.2.Table 3.1. Calculated Margins of Error for Selected Sample Sizes Sample Size (n) Margin of Error (M.E.) 200 7.1% 400 5.0% 700 3.8% 1000 3.2% 1200 2.9% 1500 2.6% 2000 2.2% 3000 1.8% 4000 1.6% 5000 1.4% Let's look at the implications of this square root relationship. To cut the margin of error in half, like from 3.2% down to 1.6%, you need four times as big of a sample, like going from 1000 to 4000 respondants. To cut the margin of error by a factor of five, you need 25 times as big of a sample, like having the margin of error go from 7.1% down to 1.4% when the sample size moves from n = 200 up to n = 5000.Figure 3.2 Relationship Between Sample Size and Margin of Error In Figure 3.2, you again find that as the sample size increases, the margin of error decreases. However, you should also notice that there is a diminishing return from taking larger and larger samples. in the table and graph, the amount by which the margin of error decreases is most substantial between samples sizes of 200 and 1500. This implies that the reliability of the estimate is more strongly affected by the size of the sample in that range. In contrast, the margin of error does not substantially decrease at sample sizes above 1500 (since it is already below 3%). It is rarely worth it for pollsters to spend additional time and money to bring the margin of error down below 3% or so. After that point, it is probably better to spend additional resources on reducing sources of bias that might be on the same order as the margin of error. An obvious exception would be in a government survey, like the one used to estimate the unemployment rate, where even tenths of a percent matter. ‹ 3.3 The Beauty of Sampling up 3.5 Simple Random Sampling and Other Sampling Methods › Printer-friendly version Navigation Start Here! Welcome to STAT 100! Faculty login (PSU Access Account) Lessons Lesson 2: Statistics: Benefits, Risks, and Measurements Lesson 3: Characteristics of Good Sample Surveys and Comparative Studies3.1 Overview 3.2 Defining a Common Lan