In this context, ( s^2 ) would refer to the sample variance of the salaries of the 66 employees taken from the population of 820 employees. It is a measure of how much the salaries of these sampled employees deviate from their average salary. This sample variance provides an estimate of the variance of the population, assuming that the sample is representative.
yes, it can be smaller, equal or larger to the true value of the population varience.
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If you know the population variance or if you have a very large sample then you could reliably use a Z test. Otherwise you should use a t test and use s^2 as an estimator for the population variance.
Sampling distribution is the probability distribution of a given sample statistic. For example, the sample mean. We could take many samples of size k and look at the mean of each of those. The means would form a distribution and that distribution has a mean, a variance and standard deviation. Now the population only has one mean, so we can't do this. Population distribution can refer to how some quality of the population is distributed among the population.
well a sample size can be any size depending on the requirements. A sample size could be 10 people of that entire population or it could be 1000 people.
The population consists of every possible unit where a sample is a subset of the population. Note that population and sample need not refer to persons. For example, if studying biodiversity, the population could consist of plots of land.
Yes. You could have a biased sample. Its distribution would not necessarily match the distribution of the parent population.
If a population is considered a sample of a larger population, it means that the characteristics and behaviors of that sample can be used to make inferences about the entire population. This approach is often employed in statistical analysis where studying the entire population is impractical. The sample should be representative to ensure that the findings are valid and reliable. Proper sampling methods help minimize bias and enhance the accuracy of conclusions drawn about the larger population.
A probability sample is one in which each member of the population has the same probability of being included. An alternative and equivalent definition is that it is a sample such that the probability of selecting that particular sample is the same for all samples of that size which could be drawn from the population.
Sample is subset of the population so sample size and population size is different.However, as a subset can be the whole set, if the sample size equals the population size, you have sampled the entire population and you will be 100% accurate with your results; it may cost much more than surveying a [representative] sample, but you get the satisfaction of knowing for what you surveyed the population exactly.Using a sample is a trade off between the cost of surveying the whole population and accuracy of the result.A census is a survey of the whole population and could be considered that the sample size = population size; in this case the results are 100% accurate.The television viewing figures are calculated using a sample of the whole population and then extrapolating them to the whole population; depending upon how the same was chosen, including its size, will affect the accuracy of the results - most likely not more than 95% accurate.With a carefully selected (that is properly biased) sample you can prove almost anything!
Population refers to all the individuals or items of interest in a particular group. Statistical population refers to the theoretical concept of all possible individuals or items that could be included in a study, from which a sample is actually drawn. Statistical population is typically larger than the actual population being studied.