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Estimating Population Standard Deviation

Estimating Population Standard Deviation

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...

Testing a Claim about Population Proportion

Testing a Claim about Population Proportion

A complete procedure for testing a claim about a population proportion is provided here.
There are two methods of testing a claim about a population proportion: (1) Using the sample proportion from the data where a binomial distribution is approximated to the normal distribution and (2) Using the binomial probabilities calculated from the data.
The first method uses normal distribution as an approximation to the binomial distribution. The requirements are as follows: sample size is large...

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...

Distributions to Estimate Population Parameter

Distributions to Estimate Population Parameter

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 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...

Estimating Population Mean with Known Standard Deviation

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)
The...

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Estimating the cohabiting population.

¹Office for National Statistics.

Population Trends

|July 18, 2009

Summary

This summary is machine-generated.

Cohabitation in England and Wales has significantly increased, with 4.5 million adults cohabiting in 2007. Future trends suggest continued growth, especially among older, never-married adults.

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Published on: July 4, 2007

Area of Science:

Sociology
Demographics
Family Studies

Background:

Cohabitation has become increasingly prevalent in England and Wales over the past fifteen years.
Previous estimates showed 2.7 million cohabiting adults in 1992, representing 6% of the adult population.

Purpose of the Study:

To summarize mid-2007 cohabitation estimates for England and Wales.
To compare current estimates with historical data and identify trends.

Main Methods:

Analysis of cohabitation estimates for England and Wales.
Comparison of 2007 data with estimates from previous years, including 1992.

Main Results:

The number of cohabiting adults in England and Wales rose to an estimated 4.5 million in 2007.
This represents 10% of the population over 16 years old, a substantial increase from 1992.
Cohabitation trends indicate continued growth, particularly for never-married adults at older ages.

Conclusions:

Cohabitation is a growing trend in England and Wales.
Future increases are expected, especially among older never-married adults.
Historic increases in cohabitation for never-married adults under 30 may be plateauing.