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Population Growth

Population Growth

Population size is dynamic, increasing with birth rates and immigration, and decreasing with death rates and emigration. In ideal conditions with unlimited resources, populations can increase exponentially, which plots as a J-shaped growth rate curve of population size against time. This type of curve is characteristic of newly-introduced invasive species, or populations that have suffered catastrophic declines and are rebounding.However, realistic environmental conditions limit the number of...

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Collecting samples or responses from an entire population takes significant time and effort, so a researcher collects responses from only a sample of that population. Suppose a study needs to collect information about a specific mobile application. After sample collection, the researcher analyzes the data and discovers that most individuals in the sample use that specific mobile application. The sample proportion measures the number of individuals in a sample who either use or don't use the...

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Estimating Population Mean with Known Standard Deviation

To construct a confidence interval for a single unknown population mean μ, where the population standard deviation is known, we need sample mean as an estimate for μ and we need the margin of error. Here, the margin of error (EBM) is called the error bound for a population mean (abbreviated EBM). The sample mean is the point estimate of the unknown population mean μ.
The confidence interval estimate will have the form as follows:
(point estimate - error bound, point estimate + error bound)
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Distributions to Estimate Population Parameter

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The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...

Estimating Population Standard Deviation

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When the population standard deviation is unknown and the sample size is large, the sample standard deviation s is commonly used as a point estimate of σ. However, it can sometimes under or overestimate the population standard deviation. To overcome this drawback, confidence intervals are determined to estimate population parameters and eliminate any calculation bias accurately. However, this only applies to random samples from normally distributed populations. Knowing the sample mean and...

Estimating Population Mean with Unknown Standard Deviation

Estimating Population Mean with Unknown Standard Deviation

In practice, we rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
William S. Gosset (1876–1937) of the Guinness...

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Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling

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Forecasting U.S. population totals with the Box-Jenkins approach.

International Journal of Forecasting

|November 1, 1992

Summary

The Box-Jenkins forecasting method is as reliable as traditional demographic approaches for long-range United States population predictions up to 2080. This statistical technique simplifies to a trend model for extended population forecasts.

Keywords:

Americas Developed Countries Estimation Technics Mathematical Model Models, Theoretical North America Northern America Population Forecast Population Projection Research Methodology United States

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Area of Science:

Demography
Statistical Modeling
Time Series Analysis

Background:

Accurate long-range population forecasting is crucial for policy and planning.
Traditional demographic methods have limitations in predicting future population trends.
Evaluating advanced statistical models for demographic projections is essential.

Purpose of the Study:

To assess the applicability and accuracy of the Box-Jenkins approach for United States population forecasting.
To compare the Box-Jenkins method's performance against traditional demographic forecasting techniques.
To determine the reliability of the Box-Jenkins method for predictions up to the year 2080.

Main Methods:

Utilized the Box-Jenkins (ARIMA) time series methodology.
Applied the model for forecasting the population of the United States.
Compared forecast accuracy with established demographic projection methods.

Main Results:

The Box-Jenkins approach was found to be equivalent to a simple trend model for long-range US population predictions.
Population forecasts generated by the Box-Jenkins method demonstrated comparable reliability to traditional demographic methods.
The study validates the use of statistical time series models for extended demographic forecasting.

Conclusions:

The Box-Jenkins method offers a reliable alternative for long-range population forecasting.
Statistical modeling, like the Box-Jenkins approach, can effectively complement traditional demographic analyses.
Future population projections for the United States can benefit from employing this robust statistical framework.