Math and Arithmetic

Statistics

Probability

123

A t-distribution with 15 degrees of freedom

See: http://en.wikipedia.org/wiki/Confidence_interval Includes a worked out example for the confidence interval of the mean of a distribution. In general, confidence intervals are calculated from the sampling distribution of a statistic. If "n" independent random variables are summed (as in the calculation of a mean), then their sampling distribution will be the t distribution with n-1 degrees of freedom.

No. For instance, when you calculate a 95% confidence interval for a parameter this should be taken to mean that, if you were to repeat the entire procedure of sampling from the population and calculating the confidence interval many times then the collection of confidence intervals would include the given parameter 95% of the time. And sometimes the confidence intervals would not include the given parameter.

The standard deviation associated with a statistic and its sampling distribution.

, the desired probabilistic level at which the obtained interval will contain the population parameter.

Yes, but that begs the question: how large should the sample size be?

Confidence intervals may be calculated for any statistics, but the most common statistics for which CI's are computed are mean, proportion and standard deviation. I have include a link, which contains a worked out example for the confidence interval of a mean.

P. van der Laan has written: 'Simple distribution-free confidence intervals for a difference in location' -- subject(s): Confidence interval, Distribution (Probability theory), Nonparametric statistics, Sampling (Statistics), Statistical hypothesis testing

The standard score associated with a given degree of confidence.

Confidence intervals represent an interval that is likely, at some confidence level, to contain the true population parameter of interest. Confidence interval is always qualified by a particular confidence level, expressed as a percentage. The end points of the confidence interval can also be referred to as confidence limits.

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 most important thing in creating intervals for a frequency distribution is that the intervals used must be non-overlapping and contain all of the possible observations. They are often equal intervals, but sometimes unequal ones are used. It all depends on the data.

Esa I. Uusipaikka has written: 'Confidence intervals in generalized regression models' -- subject(s): Regression analysis, Linear models (Mathematics), Statistics, Confidence intervals

They are related but they are NOT the same.

Confidence intervals represent a specific probability that the "true" mean of a data set falls within a given range. The given range is based off of the experimental mean.

I can examine this as a question of theory or real life: As a matter of theory, I will rephrase your question as follows: Does theoretical confidence interval of the mean (CI) of a sample, size n become larger as n is reduced? The answer is true. This is established from the sampling distribution of the mean. The sampling distribution is the probability distribution of the mean of a sample, size n. I will also consider the question as a matter of real life: If I take a sample from a population, size 50 and calculate the CI and take a smaller sample, say size 10, will I calculate a larger CI? If I use the standard deviation calculated from the sample, this is not necessarily true. The CI should be larger but I can't say in every case it will belarger. The standard deviation of the sample will vary from sample to sample. I hope this answers your question. You can find more information on confidence intervals at: http://onlinestatbook.com/chapter8/mean.html

If you are a good business man then they don't.

An open interval centered about the point estimate, .

Frequency Distribution Table

Assuming that the requirements of normality are met, a statement such as the parameter M has the value m, with a 95% confidence interval of (m-a, m+b) means that there is a 95% probability that the true value of M lies between m-a and m+b.

There are an infinite number of confidence intervals; different disciplines and different circumstances will determine which is used. Common ones are 50% (is the event likely?), 75%, 90%, 95%, 99%, 99.5%, 99.9%, 99.99% etc.

the population increases by o.5 million per age group going up of intervals of 4. (example) 0-4=1.4 million 5-9=2.0 million

The normal distribution is very important in statistical analysis. A considerable amount of data follows a normal distribution: the weight and length of items mass-produced usually follow a normal distribution ; and if average demand for a product is high, then demand usually follows a normal distribution. It is possible to show that when the sample is large, the sample mean follows a normal distribution. This result is important in the construction of confidence intervals and in significance testing. In quality control procedures for a mean chart, the construction of the warning and action lines is based on the normal distribution.

Statistical estimates cannot be exact: there is a degree of uncertainty associated with any statistical estimate. A confidence interval is a range such that the estimated value belongs to the confidence interval with the stated probability.

The confidence intervals will increase. How much it will increase depends on whether the underlying probability model is additive or multiplicative.

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