Doubling Sample Size And Standard Error
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36. What will become if you change the sample size to: a. 72 There are two ways to do this. 1.) Solve for s: is 2.40 and the sample size is 36, and since is defined as and estimated as , the standard deviation must be: Now plug the standard deviation into the equation and standard deviation double sample size get the new standard error: 2.) is defined as If you change the sample size by a factor
In General How Does Doubling The Sample Size
of c, the new will be But since you can see that: and the new will be times the old This is the "inverse square root" relation in general how does doubling the sample size change the confidence interval size between sample size and . For this example, when you make the sample size twice as big, the will be times as big, or b. 9 The new sample size is one fourth as big, so: and the new standard error will be twice
Sample Size And Standard Error Relationship
as large as the original one: c. 144 The new sample is four times as big, so: and the new standard error is half as large as the original one: 3. Assume is 3.60 and your estimate for is 9.00. Assuming your sample size does not change, what will be if you could change to: a. 12.0 Changing from 9.0 to 12.0 will increase the standard error of the mean by 12/9 = 1.33, which will give you 4.8 instead of 3.6. b. 4.5 Changing from 9.0 to 4.5 sample size standard error calculator will decrease the standard error of the mean by 4.5/9 = 0.5, which will give you 1.8 instead of 3.6. c. 13.5 Changing from 9.0 to 13.5 will increase the standard error of the mean by 13.5/9 = 1.5, which will give you 5.4 instead of 3.6. 4. If the sample's standard deviation tells you how good the sample's mean is as a description of the typical person in the sample, the standard error of the mean tell you how good the sample's mean is as a description of what? In other words, if the sample's standard deviation tells you how far the sample's mean is from the typical person in the sample, the standard error of the mean tells you how far the sample's mean is likely to be from what? How far from the population's mean. 5. Calculate for the following eleven samples: n s a. 36 6.0 1.0000 b. 36 8.0 1.3333 c. 36 12.0 2.0000 d. 49 6.0 0.8571 e. 49 8.0 1.1428 f. 72 12.0 1.4142 g. 98 6.0 0.6061 h. 98 8.0 0.8081 i. 98 12.0 1.2122 j. 144 12.0 1.0000 l. 144 8.0 0.6667 6. Examine the answers you obtained for question 5. a. What effect does doubling the sample size have on when s doesn't change? It is an inverse square relation. Multiplying the sample size by 2 divides the standard error by the square root of 2. The new will be: b. What effect does quadrupling the sample size have on when s doesn't change? Multiplying the sample size by 4 divides the standard error by t
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If The Size Of The Sample Is Increased The Standard Error Will
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Effect Of Sample Size On Standard Error
Overflow the company Business Learn more about hiring developers or posting ads with us Cross Validated Questions Tags sample size margin of error Users Badges Unanswered Ask Question _ Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. Join them; http://www.sfu.ca/~richards/Zen/Pages/Chap9.htm it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top Why does increasing the sample size lower the variance? up vote 14 down vote favorite 4 Big picture: I'm trying to understand how increasing the sample size increases the power of http://stats.stackexchange.com/questions/129885/why-does-increasing-the-sample-size-lower-the-variance an experiment. My lecturer's slides explain this with a picture of 2 normal distributions, one for the null-hypothesis and one for the alternative-hypothesis and a decision threshold c between them. They argue that increasing sample size will lower variance and thereby cause a higher kurtosis, reducing the shared area under the curves and so the probability of a type II error. Small picture: I don't understand how a bigger sample size will lower the variance. I assume you just calculate the sample variance and use it as a parameter in a normal distribution. I tried: googling, but most accepted answers have 0 upvotes or are merely examples thinking: By the law of big numbers every value should eventually stabilize around its probable value according to the normal distribution we assume. And the variance should therefore converge to the variance of our assumed normal distribution. But what is the variance of that normal distribution and is it a minimum value i.e. can we be sure our sample variance decreases to that value? variance sampling power share|improve this question asked
What Is a Confidence Interval? 3 How to Calculate the Margin of Error 4 Calculating a Confidence Interval for a Mean 5 How http://statistics.about.com/od/Inferential-Statistics/a/How-Large-Of-A-Sample-Size-Do-We-Need-For-A-Certain-Margin-Of-Error.htm to Calculate a Confidence Interval for a… About.com About Education Statistics . https://www.physicsforums.com/threads/sample-size-and-standard-deviation-of-the-sampling-distribution-of-the-mean.593928/ . . Statistics Help and Tutorials by Topic Inferential Statistics How Large of a Sample Size Do We Need for a Certain Margin of Error Students sitting at desks and writing. Frederick Bass / Getty Images By Courtney Taylor Statistics Expert Share Pin Tweet Submit Stumble Post Share sample size By Courtney Taylor Updated June 29, 2016. Confidence intervals are found in the topic of inferential statistics. The general form of such a confidence interval is an estimate, plus or minus a margin of error. One example of this is in an opinion poll in which support for an issue is gauged at a certain percent, plus or minus a given sample size and percent.Another example is when we state that at a certain level of confidence, the mean is x̄ +/- E, where E is the margin of error. This range of values is due to the nature of the statistical procedures that are done, but the calculation of the margin of error relies upon a fairly simple formula.Although we can calculate the margin of error just by knowing the sample size, population standard deviation and our desired level of confidence, we can flip the question around. What should our sample size be in order to guarantee a specified margin of error?Design of ExperimentThis sort of basic question falls under the idea of experimental design. For a particular confidence level, we can have a sample size as large or as small as we want. continue reading below our video 5 Common Dreams and What They Supposedly Mean Assuming that our standard deviation remains fixed, the margin of error is directly proportional to our critical value (which relies upon our level of confidence), and inversely proportional to the square root of the sample
Community Forums > Mathematics > Set Theory, Logic, Probability, Statistics > Dismiss Notice Join Physics Forums Today! The friendliest, high quality science and math community on the planet! Everyone who loves science is here! Sample Size and Standard Deviation of the Sampling Distribution of the Mean Apr 6, 2012 #1 nraic Hi, I am doing an undergraduate introductory statistics course and I'm trying to understand some basic concepts. I'm trying to understand why the sample size (n) affects the standard deviation of the sampling distribution of the mean (σ[itex]_{M}[/itex]) I understand how a sample size affects the sampling distribution of the mean. I've been shown that with larger sample sizes the standard deviation decreases. This can be seen graphically the normal distribution curve of the samples mean becoming more narrow as the sample size increases. σ[itex]_{M}[/itex] = σ[itex]/\sqrt{n}[/itex] What I don't understand is why this is happening. I have this intuitive feeling that if you take an infinite number of samples means they should have a fixed mean and standard deviation and that this shouldn't be different if you take samples of n=10 or n=100. I've been shown that this is wrong but I don't understand why. nraic, Apr 6, 2012 Phys.org - latest science and technology news stories on Phys.org •Game over? Computer beats human champ in ancient Chinese game •Simplifying solar cells with a new mix of materials •Imaged 'jets' reveal cerium's post-shock inner strength Apr 6, 2012 #2 chiro Science Advisor nraic said: ↑ Hi, I am doing an undergraduate introductory statistics course and I'm trying to understand some basic concepts. I'm trying to understand why the sample size (n) affects the standard deviation of the sampling distribution of the mean (σ[itex]_{M}[/itex]) I understand how a sample size affects the sampling distribution of the mean. I've been shown that with larger sample sizes the standard deviation decreases. This can be seen graphically the normal distribution curve of the samples mean becoming more narrow as the sample size increases. σ[itex]_{M}[/itex] = σ[itex]/\sqrt{n}[/itex] What I don't understand is why this is happening. I have this intuiti