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When using the distribution of sample mean to estimate the population mean what is the benefit of using larger sample sizes?
Wiki User
∙ 12y ago
The variance decreases with a larger sample so that the sample mean is likely to be closer to the population mean.
Wiki User
∙ 12y ago
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What is the the relationship between population and sample parameter and statistic?
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.
Why the normal distribution can be used as an approximation to the binomial distribution?
The central limit theorem basically states that for any distribution, the distribution of the sample means approaches a normal distribution as the sample size gets larger and larger. This allows us to use the normal distribution as an approximation to binomial, as long as the number of trials times the probability of success is greater than or equal to 5 and if you use the normal distribution as an approximation, you apply the continuity correction factor.
What is the difference between standard normal distribution table and the t distribution table?
standard normal is for a lot of data, a t distribution is more appropriate for smaller samples, extrapolating to a larger set.
What does it mean when the distribution of data is skewed to the right?
The distribution is unbalanced, because the right tail is larger than it would be if the distribution were balanced (symmetrical). Also called positive skew. See related link with diagrams that clarify this term.
What are the main qualities of a good estimator?
A "Good" estimator is the one which provides an estimate with the following qualities:Unbiasedness: An estimate is said to be an unbiased estimate of a given parameter when the expected value of that estimator can be shown to be equal to the parameter being estimated. For example, the mean of a sample is an unbiased estimate of the mean of the population from which the sample was drawn. Unbiasedness is a good quality for an estimate, since, in such a case, using weighted average of several estimates provides a better estimate than each one of those estimates. Therefore, unbiasedness allows us to upgrade our estimates. For example, if your estimates of the population mean µ are say, 10, and 11.2 from two independent samples of sizes 20, and 30 respectively, then a better estimate of the population mean µ based on both samples is [20 (10) + 30 (11.2)] (20 + 30) = 10.75.Consistency: The standard deviation of an estimate is called the standard error of that estimate. The larger the standard error the more error in your estimate. The standard deviation of an estimate is a commonly used index of the error entailed in estimating a population parameter based on the information in a random sample of size n from the entire population.An estimator is said to be "consistent" if increasing the sample size produces an estimate with smaller standard error. Therefore, your estimate is "consistent" with the sample size. That is, spending more money to obtain a larger sample produces a better estimate.Efficiency: An efficient estimate is one which has the smallest standard error among all unbiased estimators.The "best" estimator is the one which is the closest to the population parameter being estimated.
Which South American country has a larger population -- Chile or Peru?
The 2015 estimate for the population of Chile is - 18,000,000. Peru's estimate is - 31,000,000
What correlations can you observe between water supply and population distribution?
The larger the population the more the state wil need water to give to the people.
Why did some people want representation to be baed on population?
If they were represented by population the larger states would have all the legislated solely in their benefit.What about the states with a smaller population, they got less than they deserve?
Why does normal distribution occur when samples get larger?
That only happens when you sample a population that is normally distributed. In that case, the question and its answer are quite circular.
Counting the number of organisms in one area and multiplying to estimate the number in a larger area is called?
Population density is the counting of number of organisms in one area and multiplying to estimate the number in a larger area.
Does a leptokurtic distribution have a larger variance than Mesokurtic distribution?
yes
How does the number of repetitions effect the shape of the normal distribution?
When we discuss a sample drawn from a population, the larger the sample, or the large the number of repetitions of the event, the more certain we are of the mean value. So, when the normal distribution is considered the sampling distribution of the mean, then more repetitions lead to smaller values of the variance of the distribution.
How are police departments districted?
In those departments which are divided into several precincts or sub-districts (usually larger agencies) it is usually based on population distribution.
What sample size is required from a very large population to estimate a population proportion within?
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.
Does a random largely selected sample always give a better estimate of the population than a randomly selected sample?
A larger random sample will always give a better estimate of a population parameter than a smaller random sample.
What is the the relationship between population and sample parameter and statistic?
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.
Which has a larger population Houston or Omaha?
Houston has a larger population
