Examples of Finite Population Correction in the following topics:
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- For example, the sample mean is the usual estimator of a population mean.
- The standard error of the mean (i.e., of using the sample mean as a method of estimating the population mean) is the standard deviation of those sample means over all possible samples (of a given size) drawn from the population.
- The formula given above for the standard error assumes that the sample size is much smaller than the population size, so that the population can be considered to be effectively infinite in size.
- When the sampling fraction is large (approximately at 5% or more), the estimate of the error must be corrected by multiplying by a "finite population correction" to account for the added precision gained by sampling close to a larger percentage of the population.
- Paraphrase standard error, standard error of the mean, standard error correction and relative standard error.
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- The larger the margin of error, the less faith one should have that the poll's reported results are close to the "true" figures—the figures for the whole population .
- Polls typically involve taking a sample from a certain population.
- In the case of the Newsweek 2004 Presidential Election poll, the population of interest was the population of people who would vote.
- In cases where the sampling fraction exceeds 5%, analysts can adjust the margin of error using a "finite population correction" (FPC) to account for the added precision gained by sampling a larger percentage of the population.
- It holds that the FPC approaches zero as the sample size approaches the population size, which has the effect of eliminating the margin of error entirely.
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- The probability distributions describing the data-generation process are assumed to be fully described by a family of probability distributions involving only a finite number of unknown parameters.
- For example, one may assume that a population distribution has a finite mean.
- Whatever level of assumption is made, correctly calibrated inference in general requires these assumptions to be correct (i.e., that the data-generating mechanisms have been correctly specified).
- For example, incorrect "Assumptions of Normality" in the population invalidate some forms of regression-based inference.
- The use of any parametric model is viewed skeptically by most experts in sampling human populations.
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- Real gases deviate from the ideal gas law due to the finite volume occupied by individual gas particles.
- The particles of a real gas do, in fact, occupy a finite, measurable volume.
- At high pressures, the deviation from ideal behavior occurs because the finite volume that the gas molecules occupy is significant compared to the total volume of the container.
- The van der Waals equation modifies the ideal gas law to correct for this excluded volume, and is written as follows:
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- The hypergeometric distribution is a discrete probability distribution that describes the probability of $k$ successes in $n$ draws without replacement from a finite population of size $N$ containing a maximum of $K$ successes.
- The hypergeometric distribution applies to sampling without replacement from a finite population whose elements can be classified into two mutually exclusive categories like pass/fail, male/female or employed/unemployed.
- As random selections are made from the population, each subsequent draw decreases the population causing the probability of success to change with each draw.
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- Bond correct more than 0.50 of the time?
- Bond is correct, and compute the probability of being correct that many or more times given that the null hypothesis is true.
- The probability of being correct on 11 or more trials is 0.105 and the probability of being correct on 12 or more trials is 0.038.
- Bond is correct 0.75 of the time.
- Bond's true ability to be correct on 0.75 of the trials, the probability he will be correct on 12 or more trials is 0.63.
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- Correct interpretation:
- Incorrect language might try to describe the confidence interval as capturing the population parameter with a certain probability.
- Another especially important consideration of confidence intervals is that they only try to capture the population parameter.
- Confidence intervals only attempt to capture population parameters.
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- The mean of a population is denoted $\mu$, known as the population mean.
- The sample mean makes a good estimator of the population mean, as its expected value is equal to the population mean.
- For a finite population, the population mean of a property is equal to the arithmetic mean of the given property while considering every member of the population.
- For example, the population mean height is equal to the sum of the heights of every individual divided by the total number of individuals.The sample mean may differ from the population mean, especially for small samples.
- By contrast, the median income is the level at which half the population is below and half is above.
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- Population size and density are the two most important statistics scientists use to describe and understand populations.
- For example, a larger population may be more stable than a smaller population.
- Analyses of sample data enable scientists to infer population size and population density about the entire population.
- The correct quadrat size ensures counts of enough individuals to get a sample representative of the entire habitat.
- Choose the appropriate method to sample a population, given features of the organisms in that population
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- Therefore, if a population has a mean μ, then the mean of the sampling distribution of the mean is also μ.
- Given a population with a finite mean $\mu$ and a finite non-zero variance $\sigma$, the sampling distribution of the mean approaches a normal distribution with a mean of $\mu$ and a variance of $\frac{\sigma^2}{N}$ as N, the sample size, increases.
- The parent population was a uniform distribution.
- The parent population is uniform.
- The parent population is very non-normal.