The answer depends on how rare or common the selected trait is. For something that is very rare, you will need a much larger sample to get a reasonable estimate of proportion.
You can estimate a population's size when counting individuals if the density in a sample is greater than the population density.
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If the sample is not representative of the population, then the characteristics of the sample are not the characteristics of the population. Example: If I want to estimate the percentage of the population that are men, and my sample is the school's football team, my estimate would be that 100% of the population is comprised of men. What went wrong with my survey ? Simple. The football team is not a representative sample of the population, at least not as regards gender.
he population mean
Portion of the entire population used to estimate what is likely happening within a population.
A point estimate of a population parameter is a single value of a statistic. For example, the sample mean x is a point estimate of the population mean μ. Similarly, the sample proportion p is a point estimate of the population proportion P.
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The sampling proportion may be used to scale up the results from a sample to that of the population. It is also used for designing stratified sampling.
You can estimate a population's size when counting individuals if the density in a sample is greater than the population density.
The ecologist is using the mark and recapture method to estimate the population number of a certain species. This involves capturing, marking, and releasing a sample of individuals, then recapturing a new sample later to estimate the total population size based on the proportion of marked individuals in the second sample.
Not a lot. After all, the sample sd is an estimate for the population sd.
The relations depend on what measures. The sample mean is an unbiased estimate for the population mean, with maximum likelihood. The sample maximum is a lower bound for the population maximum.
Statistics is primarily used either to make predictions based on the data available or to make conclusions about a population of interest when only sample data is available. In both cases statistics tries to make sense of the uncertainty in the available data. When making predictions statisticians determine if the difference in the data points are due to chance or if there is a systematic relationship. The more the systematic relationship that is observed the better the prediction a statistician can make. The more random error that is observed the more uncertain the prediction. Statisticians can provide a measure of the uncertainty to the prediction. When making inference about a population, the statistician is trying to estimate how good a summary statistic of a sample really is at estimating a population statistic. For example, a statistician may be asked to estimate the proportion of women who smoke in the US. This is a population statistic. The only data however may be a random sample of 1000 women. By estimating the proportion of women who smoke in the random sample of 1000, a statistician can determine how likely the sample proportion is close to the population proportion. A statistician would report the sample proportion and an interval around that sample proportion. The interval would indicate with 95% or 99% certainty that the population proportion is within that interval, assuming the sample is really random. School Grades, medical fields when determining whether something works, and marketing works
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If the sample is not representative of the population, then the characteristics of the sample are not the characteristics of the population. Example: If I want to estimate the percentage of the population that are men, and my sample is the school's football team, my estimate would be that 100% of the population is comprised of men. What went wrong with my survey ? Simple. The football team is not a representative sample of the population, at least not as regards gender.