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To derive the formula for the one-sample proportion in the Z-interval, a sampling distribution of sample proportions needs to be taken into consideration. The mean of the sampling distribution of sample proportions is usually denoted as μ p ^ = P {\displaystyle \mu _{\hat {p}}=P} and its standard deviation is denoted as: [ 2 ]
Sample sizes may be evaluated by the quality of the resulting estimates, as follows. It is usually determined on the basis of the cost, time or convenience of data collection and the need for sufficient statistical power. For example, if a proportion is being estimated, one may wish to have the 95% confidence interval be
This fact is the basis of a hypothesis test, a "proportion z-test", for the value of p using x/n, the sample proportion and estimator of p, in a common test statistic. [35] For example, suppose one randomly samples n people out of a large population and ask them whether they agree with a certain statement. The proportion of people who agree ...
For example, in an opinion poll, possible sampling frames include an electoral register and a telephone directory. A probability sample is a sample in which every unit in the population has a chance (greater than zero) of being selected in the sample, and this probability can be accurately determined. The combination of these traits makes it ...
In statistics, a sampling distribution or finite-sample distribution is the probability distribution of a given random-sample-based statistic.If an arbitrarily large number of samples, each involving multiple observations (data points), were separately used in order to compute one value of a statistic (such as, for example, the sample mean or sample variance) for each sample, then the sampling ...
For example, a sample of teenagers might be divided into male and female on one hand and those who are and are not currently studying for a statistics exam on the other. For example, we hypothesize that the proportion of studying students is higher among the women than among the men, and we want to test whether any difference in proportions ...
The common example scenario for when a paired difference test is appropriate is when a single set of test subjects has something applied to them and the test is intended to check for an effect. Z-tests are appropriate for comparing means under stringent conditions regarding normality and a known standard deviation.
For the case of matched-pairs binary data, a common task is to build the confidence interval of the difference of the proportion of the matched events. For example, we might have a test for some disease, and we may want to check the results of it for some population at two points in time (1 and 2), to check if there was a change in the ...