In short, the confidence interval gives an interval around p in which an estimate p̂ is "likely" to be. As defined below, confidence level, confidence intervals, and sample sizes are all calculated with respect to this sampling distribution. For an explanation of why the sample estimate is normally distributed, study the Central Limit Theorem. The uncertainty in a given random sample (namely that is expected that the proportion estimate, p̂, is a good, but not perfect, approximation for the true proportion p) can be summarized by saying that the estimate p̂ is normally distributed with mean p and variance p(1-p)/n. However, sampling statistics can be used to calculate what are called confidence intervals, which are an indication of how close the estimate p̂ is to the true value p. it depends on the particular individuals that were sampled.
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Unfortunately, unless the full population is sampled, the estimate p̂ most likely won't equal the true value p, since p̂ suffers from sampling noise, i.e. Thus, to estimate p in the population, a sample of n individuals could be taken from the population, and the sample proportion, p̂, calculated for sampled individuals who have brown hair.
For the following, it is assumed that there is a population of individuals where some proportion, p, of the population is distinguishable from the other 1-p in some way e.g., p may be the proportion of individuals who have brown hair, while the remaining 1-p have black, blond, red, etc.
the population is sampled, and it is assumed that characteristics of the sample are representative of the overall population. In statistics, information is often inferred about a population by studying a finite number of individuals from that population, i.e. Related Standard Deviation Calculator | Probability Calculator This calculator gives out the margin of error or confidence interval of observation or survey. Leave blank if unlimited population size. This calculator computes the minimum number of necessary samples to meet the desired statistical constraints.
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