Margin Of Error For Proportions
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zc s x We can make a similar construction for a confidence interval for a population proportion. Instead of x, we can use p and instead of s,
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we use , hence, we can write the confidence interval for a large sample margin of error equation proportion as Confidence Interval Margin of Error for a Population Proportion Example 1000 randomly selected Americans were
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asked if they believed the minimum wage should be raised. 600 said yes. Construct a 95% confidence interval for the proportion of Americans who believe that the minimum wage should be raised. Solution: margin of error excel We have p = 600/1000 = .6 zc = 1.96 and n = 1000 We calculate: Hence we can conclude that between 57 and 63 percent of all Americans agree with the proposal. In other words, with a margin of error of .03 , 60% agree. Calculating n for Estimating a Mean Example Suppose that you were interested in the average number how to find margin of error with confidence interval of units that students take at a two year college to get an AA degree. Suppose you wanted to find a 95% confidence interval with a margin of error of .5 for m knowing s = 10. How many people should we ask? Solution Solving for n in Margin of Error = E = zc s/ we have E = zcs zc s = E Squaring both sides, we get We use the formula: Example A Subaru dealer wants to find out the age of their customers (for advertising purposes). They want the margin of error to be 3 years old. If they want a 90% confidence interval, how many people do they need to know about? Solution: We have E = 3, zc = 1.65 but there is no way of finding sigma exactly. They use the following reasoning: most car customers are between 16 and 68 years old hence the range is Range = 68 - 16 = 52 The range covers about four standard deviations hence one standard deviation is about s @ 52/4 = 13 We can now calculate n: Hence the dealer should sur
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Statistics Blog Calculus Matrices Practically Cheating Statistics Handbook Navigation How to Calculate Margin of Error in Easy Steps Probability and Statistics > Critical Values, Z-Tables & Hypothesis Testing > How to Calculate Margin https://www.ltcconline.net/greenl/courses/201/estimation/ciprop.htm of Error Contents (click to skip to that section): What is a Margin of Error? How to Calculate Margin of Error (video) What is a Margin of Error? The margin of error is the range of values below and above the sample statistic in a confidence interval. The confidence interval is a way to show what the uncertainty is with a certain statistic (i.e. from a poll or http://www.statisticshowto.com/how-to-calculate-margin-of-error/ survey). For example, a poll might state that there is a 98% confidence interval of 4.88 and 5.26. That means if the poll is repeated using the same techniques, 98% of the time the true population parameter (parameter vs. statistic) will fall within the interval estimates (i.e. 4.88 and 5.26) 98% of the time. What is a Margin of Error Percentage? A margin of error tells you how many percentage points your results will differ from the real population value. For example, a 95% confidence interval with a 4 percent margin of error means that your statistic will be within 4 percentage points of the real population value 95% of the time. The Margin of Error can be calculated in two ways: Margin of error = Critical value x Standard deviation Margin of error = Critical value x Standard error of the statistic Statistics Aren't Always Right! The idea behind confidence levels and margins of error is that any survey or poll will differ from the true population by a certain amount. However, confidence intervals and margins of error reflect the fact that there is room for error, so although 95% or 98% confidence with a 2 percent Margin of Error
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