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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.
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!
If I take 10 items (a small sample) from a population and calculate the standard deviation, then I take 100 items (larger sample), and calculate the standard deviation, how will my statistics change? The smaller sample could have a higher, lower or about equal the standard deviation of the larger sample. It's also possible that the smaller sample could be, by chance, closer to the standard deviation of the population. However, A properly taken larger sample will, in general, be a more reliable estimate of the standard deviation of the population than a smaller one. There are mathematical equations to show this, that in the long run, larger samples provide better estimates. This is generally but not always true. If your population is changing as you are collecting data, then a very large sample may not be representative as it takes time to collect.
If a business owner dies, the business could send out a formal letter notifying returning customers of the event. The letter should be short and to the point, and include what the plans for the business are.
Homogeneity means that the statistical properties of the variable which is being studied remain the same across the population. Heterogeneity means that they do not: it could be that the mean changes between different subsets of the population or the variance does.