Generally speaking an x% confidence interval has a margin of error of (100-x)%.
The standard deviation is used in the numerator of the margin of error calculation. As the standard deviation increases, the margin of error increases; therefore the confidence interval width increases. So, the confidence interval gets wider.
It depends on whether it is the Type I Error or the Type II Error that is increased.
The formula for margin of error is (Z*)*(Standard Deviation))/(sqrt(N)), so as N increases, the margin of error decreases. Here N went from 100 to 5000, so N has increased by 4900. This means the margin of error decreases. Since the confidence interval is the mean plus or minus the margin of error, a smaller margin of error means that the confidence interval is narrower.
The confidence interval consists of a central value and a margin of error around that value. If it is an X% confidence interval then there is a X% probability that the true value of the statistic in question lies inside the interval. Another way of looking at it is that if you took repeated samples and calculated the test statistic each time, you should expect X% of the test statistics to fall within the confidence interval.
It depends on whether it is the Type I Error or the Type II Error that is increased.
The width of the confidence interval willdecrease if you decrease the confidence level,increase if you decrease the sample sizeincrease if you decrease the margin of error.
The margin of error is dependent on the confidence interval.I'll give you examples to understand it better.We know:Confidence Interval (CI) = x(bar) ± margin of error (MOE)MOE = (z confidence)(sigma sub x bar, aka standard error of mean)When CI = 95%, MOE = (1.96)(sigma sub x bar)When CI = 90%, MOE = (1.64)(sigma sub x bar)Naturally, the margin of error will decrease as confidence level decreases.
The confidence interval radius determines the margin of error. If you want more information visit: http://en.wikipedia.org/wiki/Margin_of_error
if the confidence interval is 24.4 to 38.0 than the average is the exact middle: 31.2, and the margin of error is 6.8
All things being equal, a wider confidence interval (CI) implies a higher confidence. The higher confidence you want, the wider the CI gets. The lower confidence you want, the narrower the CI gets The point estimate will be the same, just the margin of error value changes based on the confidence you want. The formula for the CI is your point estimate +/- E or margin of error. The "E" formula contains a value for the confidence and the higher the confidence, the larger the value hence the wider the spread. In talking about the width of the CI, it is not correct to say more or less precise. You would state something like I am 95% confident that the CI contains the true value of the mean.
The margin of error increases as the level of confidence increases because the larger the expected proportion of intervals that will contain the parameter, the larger the margin of error.
The smaller the confidence interval, the more certain you are of the answers. Remember confidence level and confidence interval (margin of error) are 2 separate things. So if you are using an industry standard confidence level of 95% and 5% margin of error in a standard statistical table, then you could say, for example, with 95% certainty that 60% of those polled would vote for John McCain. Another way of saying this is even though you did not poll everyone (if you did, it would then become a very expensive census), you can say with a high degree of certainty (95% certainty) that 55% to 65% of those polled will vote for Johnny (sadly).
Confidence IntervalsConfidence interval (CI) is a parameter with a degree of confidence. Thus, 95 % CI means parameter with 95 % of confidence level. The most commonly used is 95 % confidence interval.Confidence intervals for means and proportions are calculated as follows:point estimate ± margin of error.
The mean plus or minus 2.576 (4/sqr.rt. 36)= 1.72 So take your average plus or minus 1.72 to get your confidence interval
You can't. You need an estimate of p (p-hat) q-hat = 1 - p-hat variance = square of std dev sample size n= p-hat * q-hat/variance yes you can- it would be the confidence interval X standard deviation / margin of error then square the whole thing
The margin of error is reduced.
From what I can understand, the difference is a technical one: the average person might equate one with the other.A confidence interval is defined to be an interval where you are x% sure that your true value lies.So if I estimated your weight was... 250 lbs (~113 kg or ~18 stone) but said that my confidence interval was 99% for the range of 50 lbs - 500 lbs, that could be true (but worthless).You can see how problems could arise: the larger the interval (range of values), the higher confidence I can have that the true answer is somewhere in there.But the larger my range of values, the less accurate it is as a whole - as in my earlier example, if I estimated your weight to be between 50 - 500 lbs, it would be technically correct, but useless if we were trying to figure out how many people we were trying to fit on say, the last helicopter out of Saigon.A margin of error, statistically speaking, (MoE) is simply defined (as far as I can tell) as a confidence interval of 95%.Notes:A margin of error shrinks as the sample size grows. A good way of estimating a margin of error is the expression (0.98)/(sqrt(n)), where n is the size of the sample in question.You may note that many polls in the news have a margin of error of 3.1% - this is due to the fact that many polls use 1,000 people for a nice 'round' number.A margin of error is unavoidable and ONLY REFLECTS THE SIZE OF THE SAMPLE.It does not, I repeat, not indicate any mistakes in the way the survey is carried out. A sample of 2,000,000 Adolf Hitlers would have a MoE of only 0.06% but might indicate that the continent of Europe believes in the therapeutic power of racial cleansing.Final note:Different people may use the term 'margin of error' slightly differently. Clarify, clarify, clarify!
Short answer, complex. I presume you're in a basic stats class so your dealing with something like a normal distribution however (or something else very standard). You can think of it this way... A confidence interval re-scales margin of likely error into a range. This allows you to say something along the lines, "I can say with 95% confidence that the mean/variance/whatever lies within whatever and whatever" because you're taking into account the likely error in your prediction (as long as the distribution is what you think it is and all stats are what you think they are). This is because, if you know all of the things I listed with absolute certainty, you are able to accurately predict how erroneous your prediction will be. It's because central limit theory allow you to assume statistically relevance of the sample, even given an infinite population of data. The main idea of a confidence interval is to create and interval which is likely to include a population parameter within that interval. Sample data is the source of the confidence interval. You will use your best point estimate which may be the sample mean or the sample proportion, depending on what the problems asks for. Then, you add or subtract the margin of error to get the actual interval. To compute the margin of error, you will always use or calculate a standard deviation. An example is the confidence interval for the mean. The best point estimate for the population mean is the sample mean according to the central limit theorem. So you add and subtract the margin of error from that. Now the margin of error in the case of confidence intervals for the mean is za/2 x Sigma/ Square root of n where a is 1- confidence level. For example, confidence level is 95%, a=1-.95=.05 and a/2 is .025. So we use the z score the corresponds to .025 in each tail of the standard normal distribution. This will be. z=1.96. So if Sigma is the population standard deviation, than Sigma/square root of n is called the standard error of the mean. It is the standard deviation of the sampling distribution of all the means for every possible sample of size n take from your population ( Central limit theorem again). So our confidence interval is the sample mean + or - 1.96 ( Population Standard deviation/ square root of sample size. If we don't know the population standard deviation, we use the sample one but then we must use a t distribution instead of a z one. So we replace the z score with an appropriate t score. In the case of confidence interval for a proportion, we compute and use the standard deviation of the distribution of all the proportions. Once again, the central limit theorem tells us to do this. I will post a link for that theorem. It is the key to really understanding what is going on here!
The parameters of the underlying distribution, plus the standard error of observation.
The margin of error in the Rasmussen poll is +/- 3 in which the confidence becomes 95%. These reports surveys were conducted by Pulse Opinion Research LLC. lately in 26, december in the year of 2012.