# Questions tagged [finite-population]

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### Sample confidence interval

I am observing a 1/3 of a large (1 000 000) population (e.g. university students). I know that 10 000 students from my observed sample opted for a extra test. I estimate that 30 000 in total opted for ...
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### Adjusting mean for very small population size

I have survey data from 8 respondents out of a population of 10 (very small I know). I know that FPC applies as we have more than 5% of the population in the sample. I can calculate the mean for a 0-...
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### Problems with central limit theorem and bigger SE with bigger samples [duplicate]

It is said that “the finite population correction factor is used when you sample without replacement from more than 5% of a finite population. It’s needed because under these circumstances, the ...
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### Adjusting for non-response bias in a survey

Say I have a target population of 10,000 for a survey, and only 2,000 respond, because they likely feel strongly about the survey topic (either happy or angry). I have clear, abundant non-response ...
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### choosing sample size in prevalence study with a finite population

I am looking to conduct an epidemiological study on a population of 1000 individuals and need to find the appropriate sample size. So far, I have the parameters to calculate my sample size but I am a ...
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### Is the sum of the medians of two sequential events a meaningful statistic?

Say I have two types of events $A$ and $B$ which happen to an individual entity, where $A$ is necessary for $B$ to occur, and $B$ starts right away after $A$. Also say we can split up the entities ...
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### Another question regarding population proportion:

Here is the link to another question that I asked recently: The answer to my previous question very clearly proves that $\frac{P_sQ_s}{n-1}$ is the unbiased estimator of Var$\left(\frac{X}{n}\right)=$...
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### An unbiased estimate for population variance

Specifically, my notes claim that when calculating confidence intervals for population proportion $p$, the estimator for the population variance is given by $\frac{P_sQ_s}{n}$, where $P_s=\frac{X}{n}$ ...
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### Estimate number of pairs in population of known size from sample

I'm trying to estimate the number of pairs that exist in my data (specifically, these are identical, or near-identical, images). Checking for pairs is expensive and time consuming. My population size ...
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### Why does the standard deviation of the sampling distribution of the sample mean needs N >= 20n

I keep seeing sources stating, without proof, that the standard deviation of the sampling distribution of the sample mean: $$\sigma/\sqrt{n}$$ is an approximate formula that only holds if the ...
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### Bayesian estimation of number of cases given country data with variable coverage

I have a database with the number of cases for a specific disease for a number of countries. For each country I have case coverage estimates provided by the country itself, so for certain countries ...
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### Bootstrapping a sample from a finite population

Can someone point me to some reference for theory on bootstrapping a sample took from a population of known size? I am used to use Bootstrap to calculate confidence intervals of a sample when the ...
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### Variance of subsample from a distribution

I've simulated $N$ variables from a distribution $X_i \sim N(0,\sigma^2)$. I now take a subsample of size $n$ from this sample. Let the indices of this subsample be denoted $S_n$. I was wondering ...
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### R survey package: finite population correction affects point estimate in addition to the variance estimate?

Forgive me if this is an idiot question, but I believed that including a finite population correction parameter in the R survey package should only impact my variance estimates in a stratified sample (...
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### Derivation of formula for sample size of finite population

I found here the formula for computing the sample size $n$ of a finite population $N$ $$n = \frac{n_\infty}{1 + \frac{n_\infty - 1}{N}}$$ where the sample size for an infinite population $n_\infty$ ...
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### How to apply the finite correction error to adjust the required sample size

I am currently refreshing my stats knowledge where I came across the notion of the finite population correction. This notion appears when determining the sample size required to construct a confidence ...
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### Sample size as proportion of population and statistical power?

I have done a study of information request response times in order to find out whether response time differs because of characteristics of the person doing the request. The studied unit is an ...
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### Finite population correction, where does the square root come from?

The correction factor for finite populations is $\sqrt{1-\frac{n}{N}}$ (for known variance) where $n$ is the sample size and $N$ is the population size. I wonder where the square root comes from. ...
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### Confidence interval for the odds ratio in a finite population

Does it make sense to estimate a confidence interval for the odds ratio / logistic regression model when the sample size is nearly equal to population size? For example, if the sample size is 50 and ...
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### Equality of two populations

Let's have two populations $A$ and $B$. Each population has $n$ integers, where $n>=1$. Can you claim that if means are the same, i.e. $\mu_A=\mu_B$ and so is the variance $\sigma^2_A=\sigma^2_B$ ...
Consider a survey where the population being estimated is finite. Using a simple random sample, you draw $n<N$ data. The sampling fraction is $f=\frac{n}{N}$. The variance will be \$(1-f)\frac{s^...