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For a confidence level, there is a corresponding confidence interval about the mean , that is, the interval [, +] within which values of should fall with probability . ...
Factors affecting the width of the CI include the sample size, the variability in the sample, and the confidence level. [4] All else being the same, a larger sample produces a narrower confidence interval, greater variability in the sample produces a wider confidence interval, and a higher confidence level produces a wider confidence interval. [5]
The table shown on the right can be used in a two-sample t-test to estimate the sample sizes of an experimental group and a control group that are of equal size, that is, the total number of individuals in the trial is twice that of the number given, and the desired significance level is 0.05. [4]
Denoting the number of events by X, we therefore wish to find the values of the parameter p of a binomial distribution that give Pr(X = 0) ≤ 0.05. The rule can then be derived [ 2 ] either from the Poisson approximation to the binomial distribution , or from the formula (1− p ) n for the probability of zero events in the binomial distribution.
Pollsters don't have that kind of time — or money — so they use smaller samples of the population. They seek to identify representative samples in which all members of the larger group have a ...
Mathematically, the variance of the sampling mean distribution obtained is equal to the variance of the population divided by the sample size. This is because as the sample size increases, sample means cluster more closely around the population mean.
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